--- _id: '14891' abstract: - lang: eng text: We give the first mathematically rigorous justification of the local density approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy–Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the uniform electron gas energy of this density. The error involves gradient terms and justifies the use of the local density approximation in the situation where the density is very flat on sufficiently large regions in space. article_processing_charge: No article_type: original author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Elliott H. full_name: Lieb, Elliott H. last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lewin M, Lieb EH, Seiringer R. The local density approximation in density functional theory. Pure and Applied Analysis. 2020;2(1):35-73. doi:10.2140/paa.2020.2.35 apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2020). The local density approximation in density functional theory. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2020.2.35 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “ The Local Density Approximation in Density Functional Theory.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/paa.2020.2.35. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “ The local density approximation in density functional theory,” Pure and Applied Analysis, vol. 2, no. 1. Mathematical Sciences Publishers, pp. 35–73, 2020. ista: Lewin M, Lieb EH, Seiringer R. 2020. The local density approximation in density functional theory. Pure and Applied Analysis. 2(1), 35–73. mla: Lewin, Mathieu, et al. “ The Local Density Approximation in Density Functional Theory.” Pure and Applied Analysis, vol. 2, no. 1, Mathematical Sciences Publishers, 2020, pp. 35–73, doi:10.2140/paa.2020.2.35. short: M. Lewin, E.H. Lieb, R. Seiringer, Pure and Applied Analysis 2 (2020) 35–73. date_created: 2024-01-28T23:01:44Z date_published: 2020-01-01T00:00:00Z date_updated: 2024-01-29T09:01:12Z day: '01' department: - _id: RoSe doi: 10.2140/paa.2020.2.35 external_id: arxiv: - '1903.04046' intvolume: ' 2' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1903.04046 month: '01' oa: 1 oa_version: Preprint page: 35-73 publication: Pure and Applied Analysis publication_identifier: eissn: - 2578-5885 issn: - 2578-5893 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: ' The local density approximation in density functional theory' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2020' ... --- _id: '6906' abstract: - lang: eng text: We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential. acknowledgement: "We would like to thank P. T. Nam and R. Seiringer for several useful discussions and\r\nfor suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”." article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Boccato, Chiara id: 342E7E22-F248-11E8-B48F-1D18A9856A87 last_name: Boccato - first_name: Christian full_name: Brennecke, Christian last_name: Brennecke - first_name: Serena full_name: Cenatiempo, Serena last_name: Cenatiempo - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein citation: ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 2020;376:1311-1395. doi:10.1007/s00220-019-03555-9 apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-019-03555-9 chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” Communications in Mathematical Physics. Springer, 2020. https://doi.org/10.1007/s00220-019-03555-9. ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime,” Communications in Mathematical Physics, vol. 376. Springer, pp. 1311–1395, 2020. ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 376, 1311–1395. mla: Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” Communications in Mathematical Physics, vol. 376, Springer, 2020, pp. 1311–95, doi:10.1007/s00220-019-03555-9. short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395. date_created: 2019-09-24T17:30:59Z date_published: 2020-06-01T00:00:00Z date_updated: 2024-02-22T13:33:02Z day: '01' department: - _id: RoSe doi: 10.1007/s00220-019-03555-9 ec_funded: 1 external_id: arxiv: - '1812.03086' isi: - '000536053300012' intvolume: ' 376' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1812.03086 month: '06' oa: 1 oa_version: Preprint page: 1311-1395 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 376 year: '2020' ... --- _id: '15072' abstract: - lang: eng text: The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions. article_processing_charge: No article_type: original author: - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Simone full_name: Warzel, Simone last_name: Warzel citation: ama: Hainzl C, Schlein B, Seiringer R, Warzel S. Many-body quantum systems. Oberwolfach Reports. 2020;16(3):2541-2603. doi:10.4171/owr/2019/41 apa: Hainzl, C., Schlein, B., Seiringer, R., & Warzel, S. (2020). Many-body quantum systems. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/41 chicago: Hainzl, Christian, Benjamin Schlein, Robert Seiringer, and Simone Warzel. “Many-Body Quantum Systems.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/41. ieee: C. Hainzl, B. Schlein, R. Seiringer, and S. Warzel, “Many-body quantum systems,” Oberwolfach Reports, vol. 16, no. 3. European Mathematical Society, pp. 2541–2603, 2020. ista: Hainzl C, Schlein B, Seiringer R, Warzel S. 2020. Many-body quantum systems. Oberwolfach Reports. 16(3), 2541–2603. mla: Hainzl, Christian, et al. “Many-Body Quantum Systems.” Oberwolfach Reports, vol. 16, no. 3, European Mathematical Society, 2020, pp. 2541–603, doi:10.4171/owr/2019/41. short: C. Hainzl, B. Schlein, R. Seiringer, S. Warzel, Oberwolfach Reports 16 (2020) 2541–2603. date_created: 2024-03-04T11:46:12Z date_published: 2020-09-10T00:00:00Z date_updated: 2024-03-12T12:02:00Z day: '10' department: - _id: RoSe doi: 10.4171/owr/2019/41 intvolume: ' 16' issue: '3' language: - iso: eng month: '09' oa_version: None page: 2541-2603 publication: Oberwolfach Reports publication_identifier: issn: - 1660-8933 publication_status: published publisher: European Mathematical Society quality_controlled: '1' status: public title: Many-body quantum systems type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '80' abstract: - lang: eng text: 'We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Gross–Pitaevskii (GP) limit where the trap frequency ω, the temperature T, and the particle number N are related by N∼ (T/ ω) 3→ ∞ while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose–Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer.' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Deuchert A, Seiringer R, Yngvason J. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 2019;368(2):723-776. doi:10.1007/s00220-018-3239-0 apa: Deuchert, A., Seiringer, R., & Yngvason, J. (2019). Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-018-3239-0 chicago: Deuchert, Andreas, Robert Seiringer, and Jakob Yngvason. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications in Mathematical Physics. Springer, 2019. https://doi.org/10.1007/s00220-018-3239-0. ieee: A. Deuchert, R. Seiringer, and J. Yngvason, “Bose–Einstein condensation in a dilute, trapped gas at positive temperature,” Communications in Mathematical Physics, vol. 368, no. 2. Springer, pp. 723–776, 2019. ista: Deuchert A, Seiringer R, Yngvason J. 2019. Bose–Einstein condensation in a dilute, trapped gas at positive temperature. Communications in Mathematical Physics. 368(2), 723–776. mla: Deuchert, Andreas, et al. “Bose–Einstein Condensation in a Dilute, Trapped Gas at Positive Temperature.” Communications in Mathematical Physics, vol. 368, no. 2, Springer, 2019, pp. 723–76, doi:10.1007/s00220-018-3239-0. short: A. Deuchert, R. Seiringer, J. Yngvason, Communications in Mathematical Physics 368 (2019) 723–776. date_created: 2018-12-11T11:44:31Z date_published: 2019-06-01T00:00:00Z date_updated: 2023-08-24T14:27:51Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00220-018-3239-0 ec_funded: 1 external_id: isi: - '000467796800007' file: - access_level: open_access checksum: c7e9880b43ac726712c1365e9f2f73a6 content_type: application/pdf creator: dernst date_created: 2018-12-17T10:34:06Z date_updated: 2020-07-14T12:48:07Z file_id: '5688' file_name: 2018_CommunMathPhys_Deuchert.pdf file_size: 893902 relation: main_file file_date_updated: 2020-07-14T12:48:07Z has_accepted_license: '1' intvolume: ' 368' isi: 1 issue: '2' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '06' oa: 1 oa_version: Published Version page: 723-776 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '7974' quality_controlled: '1' scopus_import: '1' status: public title: Bose–Einstein condensation in a dilute, trapped gas at positive temperature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 368 year: '2019' ... --- _id: '6788' abstract: - lang: eng text: We consider the Nelson model with ultraviolet cutoff, which describes the interaction between non-relativistic particles and a positive or zero mass quantized scalar field. We take the non-relativistic particles to obey Fermi statistics and discuss the time evolution in a mean-field limit of many fermions. In this case, the limit is known to be also a semiclassical limit. We prove convergence in terms of reduced density matrices of the many-body state to a tensor product of a Slater determinant with semiclassical structure and a coherent state, which evolve according to a fermionic version of the Schrödinger–Klein–Gordon equations. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 citation: ama: Leopold NK, Petrat SP. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 2019;20(10):3471–3508. doi:10.1007/s00023-019-00828-w apa: Leopold, N. K., & Petrat, S. P. (2019). Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-019-00828-w chicago: Leopold, Nikolai K, and Sören P Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” Annales Henri Poincare. Springer Nature, 2019. https://doi.org/10.1007/s00023-019-00828-w. ieee: N. K. Leopold and S. P. Petrat, “Mean-field dynamics for the Nelson model with fermions,” Annales Henri Poincare, vol. 20, no. 10. Springer Nature, pp. 3471–3508, 2019. ista: Leopold NK, Petrat SP. 2019. Mean-field dynamics for the Nelson model with fermions. Annales Henri Poincare. 20(10), 3471–3508. mla: Leopold, Nikolai K., and Sören P. Petrat. “Mean-Field Dynamics for the Nelson Model with Fermions.” Annales Henri Poincare, vol. 20, no. 10, Springer Nature, 2019, pp. 3471–3508, doi:10.1007/s00023-019-00828-w. short: N.K. Leopold, S.P. Petrat, Annales Henri Poincare 20 (2019) 3471–3508. date_created: 2019-08-11T21:59:21Z date_published: 2019-10-01T00:00:00Z date_updated: 2023-08-29T07:09:06Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00023-019-00828-w ec_funded: 1 external_id: arxiv: - '1807.06781' isi: - '000487036900008' file: - access_level: open_access checksum: b6dbf0d837d809293d449adf77138904 content_type: application/pdf creator: dernst date_created: 2019-08-12T12:05:58Z date_updated: 2020-07-14T12:47:40Z file_id: '6801' file_name: 2019_AnnalesHenriPoincare_Leopold.pdf file_size: 681139 relation: main_file file_date_updated: 2020-07-14T12:47:40Z has_accepted_license: '1' intvolume: ' 20' isi: 1 issue: '10' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 3471–3508 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Annales Henri Poincare publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Mean-field dynamics for the Nelson model with fermions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 20 year: '2019' ... --- _id: '6840' abstract: - lang: eng text: "We discuss thermodynamic properties of harmonically trapped\r\nimperfect quantum gases. The spatial inhomogeneity of these systems imposes\r\na redefinition of the mean-field interparticle potential energy as compared\r\nto the homogeneous case. In our approach, it takes the form a\r\n2N2 ωd, where\r\nN is the number of particles, ω—the harmonic trap frequency, d—system’s\r\ndimensionality, and a is a parameter characterizing the interparticle interaction.\r\nWe provide arguments that this model corresponds to the limiting case of\r\na long-ranged interparticle potential of vanishingly small amplitude. This\r\nconclusion is drawn from a computation similar to the well-known Kac scaling\r\nprocedure, which is presented here in a form adapted to the case of an isotropic\r\nharmonic trap. We show that within the model, the imperfect gas of trapped\r\nrepulsive bosons undergoes the Bose–Einstein condensation provided d > 1.\r\nThe main result of our analysis is that in d = 1 the gas of attractive imperfect\r\nfermions with a = −aF < 0 is thermodynamically equivalent to the gas of\r\nrepulsive bosons with a = aB > 0 provided the parameters aF and aB fulfill\r\nthe relation aB + aF = \x1F. This result supplements similar recent conclusion\r\nabout thermodynamic equivalence of two-dimensional (2D) uniform imperfect\r\nrepulsive Bose and attractive Fermi gases." article_number: '063101' article_processing_charge: No author: - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy - first_name: Marek full_name: Napiórkowski, Marek last_name: Napiórkowski citation: ama: 'Mysliwy K, Napiórkowski M. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. 2019;2019(6). doi:10.1088/1742-5468/ab190d' apa: 'Mysliwy, K., & Napiórkowski, M. (2019). Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/ab190d' chicago: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing, 2019. https://doi.org/10.1088/1742-5468/ab190d.' ieee: 'K. Mysliwy and M. Napiórkowski, “Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2019, no. 6. IOP Publishing, 2019.' ista: 'Mysliwy K, Napiórkowski M. 2019. Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063101.' mla: 'Mysliwy, Krzysztof, and Marek Napiórkowski. “Thermodynamics of Inhomogeneous Imperfect Quantum Gases in Harmonic Traps.” Journal of Statistical Mechanics: Theory and Experiment, vol. 2019, no. 6, 063101, IOP Publishing, 2019, doi:10.1088/1742-5468/ab190d.' short: 'K. Mysliwy, M. Napiórkowski, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).' date_created: 2019-09-01T22:00:59Z date_published: 2019-06-13T00:00:00Z date_updated: 2023-08-29T07:19:13Z day: '13' department: - _id: RoSe doi: 10.1088/1742-5468/ab190d ec_funded: 1 external_id: arxiv: - '1810.02209' isi: - '000471650100001' intvolume: ' 2019' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1810.02209 month: '06' oa: 1 oa_version: Preprint project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: 'Journal of Statistical Mechanics: Theory and Experiment' publication_identifier: eissn: - 1742-5468 publication_status: published publisher: IOP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 2019 year: '2019' ... --- _id: '7100' abstract: - lang: eng text: We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics. acknowledgement: OA fund by IST Austria article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Maximilian full_name: Jeblick, Maximilian last_name: Jeblick - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 2019;372(1):1-69. doi:10.1007/s00220-019-03599-x apa: Jeblick, M., Leopold, N. K., & Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03599-x chicago: Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” Communications in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03599-x. ieee: M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” Communications in Mathematical Physics, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019. ista: Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69. mla: Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” Communications in Mathematical Physics, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:10.1007/s00220-019-03599-x. short: M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69. date_created: 2019-11-25T08:08:02Z date_published: 2019-11-08T00:00:00Z date_updated: 2023-09-06T10:47:43Z day: '08' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00220-019-03599-x ec_funded: 1 external_id: isi: - '000495193700002' file: - access_level: open_access checksum: cd283b475dd739e04655315abd46f528 content_type: application/pdf creator: dernst date_created: 2019-11-25T08:11:11Z date_updated: 2020-07-14T12:47:49Z file_id: '7101' file_name: 2019_CommMathPhys_Jeblick.pdf file_size: 884469 relation: main_file file_date_updated: 2020-07-14T12:47:49Z has_accepted_license: '1' intvolume: ' 372' isi: 1 issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 1-69 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Derivation of the time dependent Gross–Pitaevskii equation in two dimensions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 372 year: '2019' ... --- _id: '7413' abstract: - lang: eng text: We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of order N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s predictions. article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Boccato, Chiara id: 342E7E22-F248-11E8-B48F-1D18A9856A87 last_name: Boccato - first_name: Christian full_name: Brennecke, Christian last_name: Brennecke - first_name: Serena full_name: Cenatiempo, Serena last_name: Cenatiempo - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein citation: ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 2019;222(2):219-335. doi:10.4310/acta.2019.v222.n2.a1 apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2019). Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. International Press of Boston. https://doi.org/10.4310/acta.2019.v222.n2.a1 chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” Acta Mathematica. International Press of Boston, 2019. https://doi.org/10.4310/acta.2019.v222.n2.a1. ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory in the Gross–Pitaevskii limit,” Acta Mathematica, vol. 222, no. 2. International Press of Boston, pp. 219–335, 2019. ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335. mla: Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” Acta Mathematica, vol. 222, no. 2, International Press of Boston, 2019, pp. 219–335, doi:10.4310/acta.2019.v222.n2.a1. short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222 (2019) 219–335. date_created: 2020-01-30T09:30:41Z date_published: 2019-06-07T00:00:00Z date_updated: 2023-09-06T15:24:31Z day: '07' department: - _id: RoSe doi: 10.4310/acta.2019.v222.n2.a1 external_id: arxiv: - '1801.01389' isi: - '000495865300001' intvolume: ' 222' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1801.01389 month: '06' oa: 1 oa_version: Preprint page: 219-335 publication: Acta Mathematica publication_identifier: eissn: - 1871-2509 issn: - 0001-5962 publication_status: published publisher: International Press of Boston quality_controlled: '1' scopus_import: '1' status: public title: Bogoliubov theory in the Gross–Pitaevskii limit type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 222 year: '2019' ... --- _id: '5856' abstract: - lang: eng text: We give a bound on the ground-state energy of a system of N non-interacting fermions in a three-dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of N. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value m∗ ∗≈ 0.36 , which is the same regime for which we recently showed stability of the system. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 2019;20(4):1325–1365. doi:10.1007/s00023-018-00757-0 apa: Moser, T., & Seiringer, R. (2019). Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-00757-0 chicago: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” Annales Henri Poincare. Springer, 2019. https://doi.org/10.1007/s00023-018-00757-0. ieee: T. Moser and R. Seiringer, “Energy contribution of a point-interacting impurity in a Fermi gas,” Annales Henri Poincare, vol. 20, no. 4. Springer, pp. 1325–1365, 2019. ista: Moser T, Seiringer R. 2019. Energy contribution of a point-interacting impurity in a Fermi gas. Annales Henri Poincare. 20(4), 1325–1365. mla: Moser, Thomas, and Robert Seiringer. “Energy Contribution of a Point-Interacting Impurity in a Fermi Gas.” Annales Henri Poincare, vol. 20, no. 4, Springer, 2019, pp. 1325–1365, doi:10.1007/s00023-018-00757-0. short: T. Moser, R. Seiringer, Annales Henri Poincare 20 (2019) 1325–1365. date_created: 2019-01-20T22:59:17Z date_published: 2019-04-01T00:00:00Z date_updated: 2023-09-07T12:37:42Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00023-018-00757-0 ec_funded: 1 external_id: arxiv: - '1807.00739' isi: - '000462444300008' file: - access_level: open_access checksum: 255e42f957a8e2b10aad2499c750a8d6 content_type: application/pdf creator: dernst date_created: 2019-01-28T15:27:17Z date_updated: 2020-07-14T12:47:12Z file_id: '5894' file_name: 2019_Annales_Moser.pdf file_size: 859846 relation: main_file file_date_updated: 2020-07-14T12:47:12Z has_accepted_license: '1' intvolume: ' 20' isi: 1 issue: '4' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 1325–1365 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Annales Henri Poincare publication_identifier: issn: - '14240637' publication_status: published publisher: Springer quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Energy contribution of a point-interacting impurity in a Fermi gas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 20 year: '2019' ... --- _id: '7524' abstract: - lang: eng text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\\rho$ and inverse temperature $\\beta$ differs from the one of the non-interacting system by the correction term $4 \\pi \\rho^2 |\\ln a^2 \\rho|^{-1} (2 - [1 - \\beta_{\\mathrm{c}}/\\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\\cdot]_+ = \\max\\{ 0, \\cdot \\}$ and $\\beta_{\\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit\r\n$a^2\\rho \\ll 1$ and if $\\beta \\rho \\gtrsim 1$." article_processing_charge: No author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:191003372. apa: Deuchert, A., Mayer, S., & Seiringer, R. (n.d.). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372. ArXiv. chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372. ArXiv, n.d. ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” arXiv:1910.03372. ArXiv. ista: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. arXiv:1910.03372, . mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” ArXiv:1910.03372, ArXiv. short: A. Deuchert, S. Mayer, R. Seiringer, ArXiv:1910.03372 (n.d.). date_created: 2020-02-26T08:46:40Z date_published: 2019-10-08T00:00:00Z date_updated: 2023-09-07T13:12:41Z day: '08' department: - _id: RoSe ec_funded: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.03372 month: '10' oa: 1 oa_version: Preprint page: '61' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: arXiv:1910.03372 publication_status: draft publisher: ArXiv related_material: record: - id: '7790' relation: later_version status: public - id: '7514' relation: dissertation_contains status: public scopus_import: 1 status: public title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2019' ... --- _id: '7226' article_number: '123504' article_processing_charge: No article_type: letter_note author: - first_name: Vojkan full_name: Jaksic, Vojkan last_name: Jaksic - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Jaksic V, Seiringer R. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics. 2019;60(12). doi:10.1063/1.5138135' apa: 'Jaksic, V., & Seiringer, R. (2019). Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/1.5138135' chicago: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical Physics. AIP Publishing, 2019. https://doi.org/10.1063/1.5138135.' ieee: 'V. Jaksic and R. Seiringer, “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018,” Journal of Mathematical Physics, vol. 60, no. 12. AIP Publishing, 2019.' ista: 'Jaksic V, Seiringer R. 2019. Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018. Journal of Mathematical Physics. 60(12), 123504.' mla: 'Jaksic, Vojkan, and Robert Seiringer. “Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018.” Journal of Mathematical Physics, vol. 60, no. 12, 123504, AIP Publishing, 2019, doi:10.1063/1.5138135.' short: V. Jaksic, R. Seiringer, Journal of Mathematical Physics 60 (2019). date_created: 2020-01-05T23:00:46Z date_published: 2019-12-01T00:00:00Z date_updated: 2024-02-28T13:01:45Z day: '01' ddc: - '500' department: - _id: RoSe doi: 10.1063/1.5138135 external_id: isi: - '000505529800002' file: - access_level: open_access checksum: bbd12ad1999a9ad7ba4d3c6f2e579c22 content_type: application/pdf creator: dernst date_created: 2020-01-07T14:59:13Z date_updated: 2020-07-14T12:47:54Z file_id: '7244' file_name: 2019_JournalMathPhysics_Jaksic.pdf file_size: 1025015 relation: main_file file_date_updated: 2020-07-14T12:47:54Z has_accepted_license: '1' intvolume: ' 60' isi: 1 issue: '12' language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: Journal of Mathematical Physics publication_identifier: issn: - '00222488' publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: 'Introduction to the Special Collection: International Congress on Mathematical Physics (ICMP) 2018' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 60 year: '2019' ... --- _id: '7015' abstract: - lang: eng text: We modify the "floating crystal" trial state for the classical homogeneous electron gas (also known as jellium), in order to suppress the boundary charge fluctuations that are known to lead to a macroscopic increase of the energy. The argument is to melt a thin layer of the crystal close to the boundary and consequently replace it by an incompressible fluid. With the aid of this trial state we show that three different definitions of the ground-state energy of jellium coincide. In the first point of view the electrons are placed in a neutralizing uniform background. In the second definition there is no background but the electrons are submitted to the constraint that their density is constant, as is appropriate in density functional theory. Finally, in the third system each electron interacts with a periodic image of itself; that is, periodic boundary conditions are imposed on the interaction potential. article_number: '035127' article_processing_charge: No article_type: original author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Elliott H. full_name: Lieb, Elliott H. last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lewin M, Lieb EH, Seiringer R. Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. 2019;100(3). doi:10.1103/physrevb.100.035127 apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2019). Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.100.035127 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” Physical Review B. American Physical Society, 2019. https://doi.org/10.1103/physrevb.100.035127. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Floating Wigner crystal with no boundary charge fluctuations,” Physical Review B, vol. 100, no. 3. American Physical Society, 2019. ista: Lewin M, Lieb EH, Seiringer R. 2019. Floating Wigner crystal with no boundary charge fluctuations. Physical Review B. 100(3), 035127. mla: Lewin, Mathieu, et al. “Floating Wigner Crystal with No Boundary Charge Fluctuations.” Physical Review B, vol. 100, no. 3, 035127, American Physical Society, 2019, doi:10.1103/physrevb.100.035127. short: M. Lewin, E.H. Lieb, R. Seiringer, Physical Review B 100 (2019). date_created: 2019-11-13T08:41:48Z date_published: 2019-07-25T00:00:00Z date_updated: 2024-02-28T13:13:23Z day: '25' department: - _id: RoSe doi: 10.1103/physrevb.100.035127 ec_funded: 1 external_id: arxiv: - '1905.09138' isi: - '000477888200001' intvolume: ' 100' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1905.09138 month: '07' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Floating Wigner crystal with no boundary charge fluctuations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 100 year: '2019' ... --- _id: '11' abstract: - lang: eng text: We report on a novel strategy to derive mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. The technique combines the method of counting and the coherent state approach to study the growth of the correlations among the particles and in the radiation field. As an instructional example, we derive the Schrödinger–Klein–Gordon system of equations from the Nelson model with ultraviolet cutoff and possibly massless scalar field. In particular, we prove the convergence of the reduced density matrices (of the nonrelativistic particles and the field bosons) associated with the exact time evolution to the projectors onto the solutions of the Schrödinger–Klein–Gordon equations in trace norm. Furthermore, we derive explicit bounds on the rate of convergence of the one-particle reduced density matrix of the nonrelativistic particles in Sobolev norm. author: - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: 'Leopold NK, Pickl P. Mean-field limits of particles in interaction with quantised radiation fields. In: Vol 270. Springer; 2018:185-214. doi:10.1007/978-3-030-01602-9_9' apa: 'Leopold, N. K., & Pickl, P. (2018). Mean-field limits of particles in interaction with quantised radiation fields (Vol. 270, pp. 185–214). Presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany: Springer. https://doi.org/10.1007/978-3-030-01602-9_9' chicago: Leopold, Nikolai K, and Peter Pickl. “Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields,” 270:185–214. Springer, 2018. https://doi.org/10.1007/978-3-030-01602-9_9. ieee: 'N. K. Leopold and P. Pickl, “Mean-field limits of particles in interaction with quantised radiation fields,” presented at the MaLiQS: Macroscopic Limits of Quantum Systems, Munich, Germany, 2018, vol. 270, pp. 185–214.' ista: 'Leopold NK, Pickl P. 2018. Mean-field limits of particles in interaction with quantised radiation fields. MaLiQS: Macroscopic Limits of Quantum Systems vol. 270, 185–214.' mla: Leopold, Nikolai K., and Peter Pickl. Mean-Field Limits of Particles in Interaction with Quantised Radiation Fields. Vol. 270, Springer, 2018, pp. 185–214, doi:10.1007/978-3-030-01602-9_9. short: N.K. Leopold, P. Pickl, in:, Springer, 2018, pp. 185–214. conference: end_date: 2017-04-01 location: Munich, Germany name: 'MaLiQS: Macroscopic Limits of Quantum Systems' start_date: 2017-03-30 date_created: 2018-12-11T11:44:08Z date_published: 2018-10-27T00:00:00Z date_updated: 2021-01-12T06:48:16Z day: '27' department: - _id: RoSe doi: 10.1007/978-3-030-01602-9_9 ec_funded: 1 external_id: arxiv: - '1806.10843' intvolume: ' 270' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.10843 month: '10' oa: 1 oa_version: Preprint page: 185 - 214 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_status: published publisher: Springer publist_id: '8045' quality_controlled: '1' scopus_import: 1 status: public title: Mean-field limits of particles in interaction with quantised radiation fields type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 270 year: '2018' ... --- _id: '554' abstract: - lang: eng text: We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.). author: - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Robin full_name: Reuvers, Robin last_name: Reuvers - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: 'Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 2018;360(1):347-403. doi:10.1007/s00220-017-3064-x' apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-017-3064-x' chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” Communications in Mathematical Physics. Springer, 2018. https://doi.org/10.1007/s00220-017-3064-x.' ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy functional II: The dilute Limit,” Communications in Mathematical Physics, vol. 360, no. 1. Springer, pp. 347–403, 2018.' ista: 'Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.' mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” Communications in Mathematical Physics, vol. 360, no. 1, Springer, 2018, pp. 347–403, doi:10.1007/s00220-017-3064-x.' short: M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403. date_created: 2018-12-11T11:47:09Z date_published: 2018-05-01T00:00:00Z date_updated: 2021-01-12T08:02:35Z day: '01' department: - _id: RoSe doi: 10.1007/s00220-017-3064-x external_id: arxiv: - '1511.05953' intvolume: ' 360' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1511.05953 month: '05' oa: 1 oa_version: Submitted Version page: 347-403 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Communications in Mathematical Physics publication_identifier: issn: - '00103616' publication_status: published publisher: Springer publist_id: '7260' quality_controlled: '1' scopus_import: 1 status: public title: 'The Bogoliubov free energy functional II: The dilute Limit' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 360 year: '2018' ... --- _id: '399' abstract: - lang: eng text: Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm. acknowledgement: We thank Robert Seiringer and Daniel Ueltschi for bringing the issue of the change in critical temperature to our attention. We also thank the Erwin Schrödinger Institute (all authors) and the Department of Mathematics, University of Copenhagen (MN) for the hospitality during the period this work was carried out. We gratefully acknowledge the financial support by the European Unions Seventh Framework Programme under the ERC Grant Agreement Nos. 321029 (JPS and RR) and 337603 (RR) as well as support by the VIL-LUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059) (JPS and RR), by the National Science Center (NCN) under grant No. 2016/21/D/ST1/02430 and the Austrian Science Fund (FWF) through project No. P 27533-N27 (MN). article_number: '10007' article_processing_charge: No article_type: original author: - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Robin full_name: Reuvers, Robin last_name: Reuvers - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: Napiórkowski MM, Reuvers R, Solovej J. Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation. EPL. 2018;121(1). doi:10.1209/0295-5075/121/10007 apa: Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation. EPL. IOP Publishing Ltd. https://doi.org/10.1209/0295-5075/121/10007 chicago: Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “Calculation of the Critical Temperature of a Dilute Bose Gas in the Bogoliubov Approximation.” EPL. IOP Publishing Ltd., 2018. https://doi.org/10.1209/0295-5075/121/10007. ieee: M. M. Napiórkowski, R. Reuvers, and J. Solovej, “Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation,” EPL, vol. 121, no. 1. IOP Publishing Ltd., 2018. ista: Napiórkowski MM, Reuvers R, Solovej J. 2018. Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation. EPL. 121(1), 10007. mla: Napiórkowski, Marcin M., et al. “Calculation of the Critical Temperature of a Dilute Bose Gas in the Bogoliubov Approximation.” EPL, vol. 121, no. 1, 10007, IOP Publishing Ltd., 2018, doi:10.1209/0295-5075/121/10007. short: M.M. Napiórkowski, R. Reuvers, J. Solovej, EPL 121 (2018). date_created: 2018-12-11T11:46:15Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-08T13:30:51Z day: '01' department: - _id: RoSe doi: 10.1209/0295-5075/121/10007 external_id: arxiv: - '1706.01822' isi: - '000460003000003' intvolume: ' 121' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.01822 month: '01' oa: 1 oa_version: Preprint project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: EPL publication_status: published publisher: IOP Publishing Ltd. publist_id: '7432' quality_controlled: '1' scopus_import: '1' status: public title: Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 121 year: '2018' ... --- _id: '295' abstract: - lang: eng text: We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter (Formula presented.). The lower bounds extend to Lieb–Thirring inequalities for all anyons except bosons. acknowledgement: Financial support from the Swedish Research Council, grant no. 2013-4734 (D. L.), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694227, R. S.), and by the Austrian Science Fund (FWF), project Nr. P 27533-N27 (R. S.), is gratefully acknowledged. article_processing_charge: No author: - first_name: Douglas full_name: Lundholm, Douglas last_name: Lundholm - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lundholm D, Seiringer R. Fermionic behavior of ideal anyons. Letters in Mathematical Physics. 2018;108(11):2523-2541. doi:10.1007/s11005-018-1091-y apa: Lundholm, D., & Seiringer, R. (2018). Fermionic behavior of ideal anyons. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-018-1091-y chicago: Lundholm, Douglas, and Robert Seiringer. “Fermionic Behavior of Ideal Anyons.” Letters in Mathematical Physics. Springer, 2018. https://doi.org/10.1007/s11005-018-1091-y. ieee: D. Lundholm and R. Seiringer, “Fermionic behavior of ideal anyons,” Letters in Mathematical Physics, vol. 108, no. 11. Springer, pp. 2523–2541, 2018. ista: Lundholm D, Seiringer R. 2018. Fermionic behavior of ideal anyons. Letters in Mathematical Physics. 108(11), 2523–2541. mla: Lundholm, Douglas, and Robert Seiringer. “Fermionic Behavior of Ideal Anyons.” Letters in Mathematical Physics, vol. 108, no. 11, Springer, 2018, pp. 2523–41, doi:10.1007/s11005-018-1091-y. short: D. Lundholm, R. Seiringer, Letters in Mathematical Physics 108 (2018) 2523–2541. date_created: 2018-12-11T11:45:40Z date_published: 2018-05-11T00:00:00Z date_updated: 2023-09-11T14:01:57Z day: '11' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-018-1091-y ec_funded: 1 external_id: arxiv: - '1712.06218' isi: - '000446491500008' file: - access_level: open_access checksum: 8beb9632fa41bbd19452f55f31286a31 content_type: application/pdf creator: dernst date_created: 2018-12-17T12:14:17Z date_updated: 2020-07-14T12:45:55Z file_id: '5698' file_name: 2018_LettMathPhys_Lundholm.pdf file_size: 551996 relation: main_file file_date_updated: 2020-07-14T12:45:55Z has_accepted_license: '1' intvolume: ' 108' isi: 1 issue: '11' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 2523-2541 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '7586' quality_controlled: '1' scopus_import: '1' status: public title: Fermionic behavior of ideal anyons tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 108 year: '2018' ... --- _id: '400' abstract: - lang: eng text: We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum, our results carry over to the three-dimensional case. article_processing_charge: Yes (via OA deal) author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Alissa full_name: Geisinge, Alissa last_name: Geisinge - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Michael full_name: Loss, Michael last_name: Loss citation: ama: Deuchert A, Geisinge A, Hainzl C, Loss M. Persistence of translational symmetry in the BCS model with radial pair interaction. Annales Henri Poincare. 2018;19(5):1507-1527. doi:10.1007/s00023-018-0665-7 apa: Deuchert, A., Geisinge, A., Hainzl, C., & Loss, M. (2018). Persistence of translational symmetry in the BCS model with radial pair interaction. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-018-0665-7 chicago: Deuchert, Andreas, Alissa Geisinge, Christian Hainzl, and Michael Loss. “Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction.” Annales Henri Poincare. Springer, 2018. https://doi.org/10.1007/s00023-018-0665-7. ieee: A. Deuchert, A. Geisinge, C. Hainzl, and M. Loss, “Persistence of translational symmetry in the BCS model with radial pair interaction,” Annales Henri Poincare, vol. 19, no. 5. Springer, pp. 1507–1527, 2018. ista: Deuchert A, Geisinge A, Hainzl C, Loss M. 2018. Persistence of translational symmetry in the BCS model with radial pair interaction. Annales Henri Poincare. 19(5), 1507–1527. mla: Deuchert, Andreas, et al. “Persistence of Translational Symmetry in the BCS Model with Radial Pair Interaction.” Annales Henri Poincare, vol. 19, no. 5, Springer, 2018, pp. 1507–27, doi:10.1007/s00023-018-0665-7. short: A. Deuchert, A. Geisinge, C. Hainzl, M. Loss, Annales Henri Poincare 19 (2018) 1507–1527. date_created: 2018-12-11T11:46:15Z date_published: 2018-05-01T00:00:00Z date_updated: 2023-09-15T12:04:15Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00023-018-0665-7 ec_funded: 1 external_id: isi: - '000429799900008' file: - access_level: open_access checksum: 04d2c9bd7cbf3ca1d7acaaf4e7dca3e5 content_type: application/pdf creator: system date_created: 2018-12-12T10:12:47Z date_updated: 2020-07-14T12:46:22Z file_id: '4966' file_name: IST-2018-1011-v1+1_2018_Deuchert_Persistence.pdf file_size: 582680 relation: main_file file_date_updated: 2020-07-14T12:46:22Z has_accepted_license: '1' intvolume: ' 19' isi: 1 issue: '5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 1507 - 1527 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Annales Henri Poincare publication_status: published publisher: Springer publist_id: '7429' pubrep_id: '1011' quality_controlled: '1' scopus_import: '1' status: public title: Persistence of translational symmetry in the BCS model with radial pair interaction tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 19 year: '2018' ... --- _id: '154' abstract: - lang: eng text: We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for m∈[m2,m2−1]. So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). article_number: '19' article_processing_charge: No article_type: original author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. 2018;21(3). doi:10.1007/s11040-018-9275-3 apa: Moser, T., & Seiringer, R. (2018). Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-018-9275-3 chicago: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System with Point Interactions.” Mathematical Physics Analysis and Geometry. Springer, 2018. https://doi.org/10.1007/s11040-018-9275-3. ieee: T. Moser and R. Seiringer, “Stability of the 2+2 fermionic system with point interactions,” Mathematical Physics Analysis and Geometry, vol. 21, no. 3. Springer, 2018. ista: Moser T, Seiringer R. 2018. Stability of the 2+2 fermionic system with point interactions. Mathematical Physics Analysis and Geometry. 21(3), 19. mla: Moser, Thomas, and Robert Seiringer. “Stability of the 2+2 Fermionic System with Point Interactions.” Mathematical Physics Analysis and Geometry, vol. 21, no. 3, 19, Springer, 2018, doi:10.1007/s11040-018-9275-3. short: T. Moser, R. Seiringer, Mathematical Physics Analysis and Geometry 21 (2018). date_created: 2018-12-11T11:44:55Z date_published: 2018-09-01T00:00:00Z date_updated: 2023-09-19T09:31:15Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s11040-018-9275-3 ec_funded: 1 external_id: isi: - '000439639700001' file: - access_level: open_access checksum: 411c4db5700d7297c9cd8ebc5dd29091 content_type: application/pdf creator: dernst date_created: 2018-12-17T16:49:02Z date_updated: 2020-07-14T12:45:01Z file_id: '5729' file_name: 2018_MathPhysics_Moser.pdf file_size: 496973 relation: main_file file_date_updated: 2020-07-14T12:45:01Z has_accepted_license: '1' intvolume: ' 21' isi: 1 issue: '3' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Mathematical Physics Analysis and Geometry publication_identifier: eissn: - '15729656' issn: - '13850172' publication_status: published publisher: Springer publist_id: '7767' quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Stability of the 2+2 fermionic system with point interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 21 year: '2018' ... --- _id: '455' abstract: - lang: eng text: The derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). The authors acknowledge support by ERC Advanced Grant 321029 and by VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). The authors would like to thank Sébastien Breteaux, Enno Lenzmann, Mathieu Lewin and Jochen Schmid for comments and discussions about well-posedness of the Bogoliubov–de Gennes equations. alternative_title: - Annales Henri Poincare article_processing_charge: No author: - first_name: Niels P full_name: Benedikter, Niels P id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87 last_name: Benedikter orcid: 0000-0002-1071-6091 - first_name: Jérémy full_name: Sok, Jérémy last_name: Sok - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: Benedikter NP, Sok J, Solovej J. The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare. 2018;19(4):1167-1214. doi:10.1007/s00023-018-0644-z apa: Benedikter, N. P., Sok, J., & Solovej, J. (2018). The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-018-0644-z chicago: Benedikter, Niels P, Jérémy Sok, and Jan Solovej. “The Dirac–Frenkel Principle for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” Annales Henri Poincare. Birkhäuser, 2018. https://doi.org/10.1007/s00023-018-0644-z. ieee: N. P. Benedikter, J. Sok, and J. Solovej, “The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations,” Annales Henri Poincare, vol. 19, no. 4. Birkhäuser, pp. 1167–1214, 2018. ista: Benedikter NP, Sok J, Solovej J. 2018. The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations. Annales Henri Poincare. 19(4), 1167–1214. mla: Benedikter, Niels P., et al. “The Dirac–Frenkel Principle for Reduced Density Matrices and the Bogoliubov–de Gennes Equations.” Annales Henri Poincare, vol. 19, no. 4, Birkhäuser, 2018, pp. 1167–214, doi:10.1007/s00023-018-0644-z. short: N.P. Benedikter, J. Sok, J. Solovej, Annales Henri Poincare 19 (2018) 1167–1214. date_created: 2018-12-11T11:46:34Z date_published: 2018-04-01T00:00:00Z date_updated: 2023-09-19T10:07:41Z day: '01' ddc: - '510' - '539' department: - _id: RoSe doi: 10.1007/s00023-018-0644-z external_id: isi: - '000427578900006' file: - access_level: open_access checksum: 883eeccba8384ad7fcaa28761d99a0fa content_type: application/pdf creator: system date_created: 2018-12-12T10:11:57Z date_updated: 2020-07-14T12:46:31Z file_id: '4914' file_name: IST-2018-993-v1+1_2018_Benedikter_Dirac.pdf file_size: 923252 relation: main_file file_date_updated: 2020-07-14T12:46:31Z has_accepted_license: '1' intvolume: ' 19' isi: 1 issue: '4' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 1167 - 1214 publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '7367' pubrep_id: '993' quality_controlled: '1' scopus_import: '1' status: public title: The Dirac–Frenkel principle for reduced density matrices and the Bogoliubov–de Gennes equations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 19 year: '2018' ... --- _id: '446' abstract: - lang: eng text: We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential. acknowledgement: "We thank the referee for helpful suggestions that improved the presentation of the paper. We also acknowledge partial support by National Science Foundation Grant DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática” (H.V.D.B.).\r\n" article_processing_charge: No article_type: original author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Nam full_name: Phan Thanh, Nam id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Phan Thanh - first_name: Hanne full_name: Van Den Bosch, Hanne last_name: Van Den Bosch citation: ama: Frank R, Nam P, Van Den Bosch H. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 2018;71(3):577-614. doi:10.1002/cpa.21717 apa: Frank, R., Nam, P., & Van Den Bosch, H. (2018). The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21717 chicago: Frank, Rupert, Phan Nam, and Hanne Van Den Bosch. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2018. https://doi.org/10.1002/cpa.21717. ieee: R. Frank, P. Nam, and H. Van Den Bosch, “The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory,” Communications on Pure and Applied Mathematics, vol. 71, no. 3. Wiley-Blackwell, pp. 577–614, 2018. ista: Frank R, Nam P, Van Den Bosch H. 2018. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 71(3), 577–614. mla: Frank, Rupert, et al. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” Communications on Pure and Applied Mathematics, vol. 71, no. 3, Wiley-Blackwell, 2018, pp. 577–614, doi:10.1002/cpa.21717. short: R. Frank, P. Nam, H. Van Den Bosch, Communications on Pure and Applied Mathematics 71 (2018) 577–614. date_created: 2018-12-11T11:46:31Z date_published: 2018-03-01T00:00:00Z date_updated: 2023-09-19T10:09:40Z day: '01' department: - _id: RoSe doi: 10.1002/cpa.21717 external_id: arxiv: - '1606.07355' isi: - '000422675800004' intvolume: ' 71' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1606.07355 month: '03' oa: 1 oa_version: Preprint page: 577 - 614 publication: Communications on Pure and Applied Mathematics publication_status: published publisher: Wiley-Blackwell publist_id: '7377' quality_controlled: '1' status: public title: The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 71 year: '2018' ... --- _id: '5983' abstract: - lang: eng text: We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a “rotating polaron,” which can be used to model, e.g., a rotating molecule immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian of the rotating polaron and study its spectrum in the weak- and strong-coupling regimes using a combination of variational, diagrammatic, and mean-field approaches. We reveal how the coupling between linear and angular momenta affects stable quasiparticle states, and demonstrate that internal rotation leads to an enhanced self-localization in the translational degrees of freedom. article_number: '224506' article_processing_charge: No author: - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 - first_name: Bikashkali full_name: Midya, Bikashkali id: 456187FC-F248-11E8-B48F-1D18A9856A87 last_name: Midya - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Nikolai K full_name: Leopold, Nikolai K id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87 last_name: Leopold orcid: 0000-0002-0495-6822 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 citation: ama: 'Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. Theory of the rotating polaron: Spectrum and self-localization. Physical Review B. 2018;98(22). doi:10.1103/physrevb.98.224506' apa: 'Yakaboylu, E., Midya, B., Deuchert, A., Leopold, N. K., & Lemeshko, M. (2018). Theory of the rotating polaron: Spectrum and self-localization. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.98.224506' chicago: 'Yakaboylu, Enderalp, Bikashkali Midya, Andreas Deuchert, Nikolai K Leopold, and Mikhail Lemeshko. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” Physical Review B. American Physical Society, 2018. https://doi.org/10.1103/physrevb.98.224506.' ieee: 'E. Yakaboylu, B. Midya, A. Deuchert, N. K. Leopold, and M. Lemeshko, “Theory of the rotating polaron: Spectrum and self-localization,” Physical Review B, vol. 98, no. 22. American Physical Society, 2018.' ista: 'Yakaboylu E, Midya B, Deuchert A, Leopold NK, Lemeshko M. 2018. Theory of the rotating polaron: Spectrum and self-localization. Physical Review B. 98(22), 224506.' mla: 'Yakaboylu, Enderalp, et al. “Theory of the Rotating Polaron: Spectrum and Self-Localization.” Physical Review B, vol. 98, no. 22, 224506, American Physical Society, 2018, doi:10.1103/physrevb.98.224506.' short: E. Yakaboylu, B. Midya, A. Deuchert, N.K. Leopold, M. Lemeshko, Physical Review B 98 (2018). date_created: 2019-02-14T10:37:09Z date_published: 2018-12-12T00:00:00Z date_updated: 2023-09-19T14:29:03Z day: '12' department: - _id: MiLe - _id: RoSe doi: 10.1103/physrevb.98.224506 ec_funded: 1 external_id: arxiv: - '1809.01204' isi: - '000452992700008' intvolume: ' 98' isi: 1 issue: '22' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1809.01204 month: '12' oa: 1 oa_version: Preprint project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: 'Theory of the rotating polaron: Spectrum and self-localization' type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 98 year: '2018' ... --- _id: '6002' abstract: - lang: eng text: The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation-invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove the existence of a phase transition in this model and provide its phase diagram. article_processing_charge: No author: - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Robin full_name: Reuvers, Robin last_name: Reuvers - first_name: Jan Philip full_name: Solovej, Jan Philip last_name: Solovej citation: ama: 'Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. Archive for Rational Mechanics and Analysis. 2018;229(3):1037-1090. doi:10.1007/s00205-018-1232-6' apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. P. (2018). The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-018-1232-6' chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” Archive for Rational Mechanics and Analysis. Springer Nature, 2018. https://doi.org/10.1007/s00205-018-1232-6.' ieee: 'M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy functional I: Existence of minimizers and phase diagram,” Archive for Rational Mechanics and Analysis, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.' ista: 'Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. Archive for Rational Mechanics and Analysis. 229(3), 1037–1090.' mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” Archive for Rational Mechanics and Analysis, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:10.1007/s00205-018-1232-6.' short: M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090. date_created: 2019-02-14T13:40:53Z date_published: 2018-09-01T00:00:00Z date_updated: 2023-09-19T14:33:12Z day: '01' department: - _id: RoSe doi: 10.1007/s00205-018-1232-6 external_id: arxiv: - '1511.05935' isi: - '000435367300003' intvolume: ' 229' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1511.05935 month: '09' oa: 1 oa_version: Preprint page: 1037-1090 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'The Bogoliubov free energy functional I: Existence of minimizers and phase diagram' type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 229 year: '2018' ... --- _id: '52' abstract: - lang: eng text: In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser citation: ama: Moser T. Point interactions in systems of fermions. 2018. doi:10.15479/AT:ISTA:th_1043 apa: Moser, T. (2018). Point interactions in systems of fermions. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th_1043 chicago: Moser, Thomas. “Point Interactions in Systems of Fermions.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:th_1043. ieee: T. Moser, “Point interactions in systems of fermions,” Institute of Science and Technology Austria, 2018. ista: Moser T. 2018. Point interactions in systems of fermions. Institute of Science and Technology Austria. mla: Moser, Thomas. Point Interactions in Systems of Fermions. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:th_1043. short: T. Moser, Point Interactions in Systems of Fermions, Institute of Science and Technology Austria, 2018. date_created: 2018-12-11T11:44:22Z date_published: 2018-09-04T00:00:00Z date_updated: 2023-09-27T12:34:14Z day: '04' ddc: - '515' - '530' - '519' degree_awarded: PhD department: - _id: RoSe doi: 10.15479/AT:ISTA:th_1043 file: - access_level: open_access checksum: fbd8c747d148b468a21213b7cf175225 content_type: application/pdf creator: dernst date_created: 2019-04-09T07:45:38Z date_updated: 2020-07-14T12:46:37Z file_id: '6256' file_name: 2018_Thesis_Moser.pdf file_size: 851164 relation: main_file - access_level: closed checksum: c28e16ecfc1126d3ce324ec96493c01e content_type: application/zip creator: dernst date_created: 2019-04-09T07:45:38Z date_updated: 2020-07-14T12:46:37Z file_id: '6257' file_name: 2018_Thesis_Moser_Source.zip file_size: 1531516 relation: source_file file_date_updated: 2020-07-14T12:46:37Z has_accepted_license: '1' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: '115' project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '8002' pubrep_id: '1043' related_material: record: - id: '5856' relation: part_of_dissertation status: public - id: '154' relation: part_of_dissertation status: public - id: '1198' relation: part_of_dissertation status: public - id: '741' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Point interactions in systems of fermions type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '180' abstract: - lang: eng text: In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density. acknowledgement: "This project has received funding from the European Research Council (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme (grant agreement 694227 for R.S. and MDFT 725528 for M.L.). Financial support by the Austrian Science Fund (FWF), project No P 27533-N27 (R.S.) and by the US National Science Foundation, grant No PHY12-1265118 (E.H.L.) are gratefully acknowledged." article_processing_charge: No article_type: original author: - first_name: Mathieu full_name: Lewi, Mathieu last_name: Lewi - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Lewi M, Lieb É, Seiringer R. Statistical mechanics of the uniform electron gas. Journal de l’Ecole Polytechnique - Mathematiques. 2018;5:79-116. doi:10.5802/jep.64 apa: Lewi, M., Lieb, É., & Seiringer, R. (2018). Statistical mechanics of the uniform electron gas. Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.64 chicago: Lewi, Mathieu, Élliott Lieb, and Robert Seiringer. “Statistical Mechanics of the Uniform Electron Gas.” Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique, 2018. https://doi.org/10.5802/jep.64. ieee: M. Lewi, É. Lieb, and R. Seiringer, “Statistical mechanics of the uniform electron gas,” Journal de l’Ecole Polytechnique - Mathematiques, vol. 5. Ecole Polytechnique, pp. 79–116, 2018. ista: Lewi M, Lieb É, Seiringer R. 2018. Statistical mechanics of the uniform electron gas. Journal de l’Ecole Polytechnique - Mathematiques. 5, 79–116. mla: Lewi, Mathieu, et al. “Statistical Mechanics of the Uniform Electron Gas.” Journal de l’Ecole Polytechnique - Mathematiques, vol. 5, Ecole Polytechnique, 2018, pp. 79–116, doi:10.5802/jep.64. short: M. Lewi, É. Lieb, R. Seiringer, Journal de l’Ecole Polytechnique - Mathematiques 5 (2018) 79–116. date_created: 2018-12-11T11:45:03Z date_published: 2018-07-01T00:00:00Z date_updated: 2023-10-17T08:05:28Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.5802/jep.64 ec_funded: 1 external_id: arxiv: - '1705.10676' file: - access_level: open_access checksum: 1ba7cccdf3900f42c4f715ae75d6813c content_type: application/pdf creator: dernst date_created: 2018-12-17T16:38:18Z date_updated: 2020-07-14T12:45:16Z file_id: '5726' file_name: 2018_JournaldeLecoleMath_Lewi.pdf file_size: 843938 relation: main_file file_date_updated: 2020-07-14T12:45:16Z has_accepted_license: '1' intvolume: ' 5' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '07' oa: 1 oa_version: Published Version page: 79 - 116 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Journal de l'Ecole Polytechnique - Mathematiques publication_identifier: eissn: - 2270-518X issn: - 2429-7100 publication_status: published publisher: Ecole Polytechnique publist_id: '7741' quality_controlled: '1' scopus_import: '1' status: public title: Statistical mechanics of the uniform electron gas tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2018' ... --- _id: '484' abstract: - lang: eng text: We consider the dynamics of a large quantum system of N identical bosons in 3D interacting via a two-body potential of the form N3β-1w(Nβ(x - y)). For fixed 0 = β < 1/3 and large N, we obtain a norm approximation to the many-body evolution in the Nparticle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory. author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski citation: ama: Nam P, Napiórkowski MM. Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. 2017;21(3):683-738. doi:10.4310/ATMP.2017.v21.n3.a4 apa: Nam, P., & Napiórkowski, M. M. (2017). Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a4 chicago: Nam, Phan, and Marcin M Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a4. ieee: P. Nam and M. M. Napiórkowski, “Bogoliubov correction to the mean-field dynamics of interacting bosons,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 683–738, 2017. ista: Nam P, Napiórkowski MM. 2017. Bogoliubov correction to the mean-field dynamics of interacting bosons. Advances in Theoretical and Mathematical Physics. 21(3), 683–738. mla: Nam, Phan, and Marcin M. Napiórkowski. “Bogoliubov Correction to the Mean-Field Dynamics of Interacting Bosons.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 683–738, doi:10.4310/ATMP.2017.v21.n3.a4. short: P. Nam, M.M. Napiórkowski, Advances in Theoretical and Mathematical Physics 21 (2017) 683–738. date_created: 2018-12-11T11:46:43Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:00:58Z day: '01' department: - _id: RoSe doi: 10.4310/ATMP.2017.v21.n3.a4 ec_funded: 1 intvolume: ' 21' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1509.04631 month: '01' oa: 1 oa_version: Submitted Version page: 683 - 738 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Advances in Theoretical and Mathematical Physics publication_identifier: issn: - '10950761' publication_status: published publisher: International Press publist_id: '7336' quality_controlled: '1' scopus_import: 1 status: public title: Bogoliubov correction to the mean-field dynamics of interacting bosons type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2017' ... --- _id: '632' abstract: - lang: eng text: 'We consider a 2D quantum system of N bosons in a trapping potential |x|s, interacting via a pair potential of the form N2β−1 w(Nβ x). We show that for all 0 < β < (s + 1)/(s + 2), the leading order behavior of ground states of the many-body system is described in the large N limit by the corresponding cubic nonlinear Schrödinger energy functional. Our result covers the focusing case (w < 0) where even the stability of the many-body system is not obvious. This answers an open question mentioned by X. Chen and J. Holmer for harmonic traps (s = 2). Together with the BBGKY hierarchy approach used by these authors, our result implies the convergence of the many-body quantum dynamics to the focusing NLS equation with harmonic trap for all 0 < β < 3/4. ' author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Nicolas full_name: Rougerie, Nicolas last_name: Rougerie citation: ama: Lewin M, Nam P, Rougerie N. A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. 2017;145(6):2441-2454. doi:10.1090/proc/13468 apa: Lewin, M., Nam, P., & Rougerie, N. (2017). A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/13468 chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “A Note on 2D Focusing Many Boson Systems.” Proceedings of the American Mathematical Society. American Mathematical Society, 2017. https://doi.org/10.1090/proc/13468. ieee: M. Lewin, P. Nam, and N. Rougerie, “A note on 2D focusing many boson systems,” Proceedings of the American Mathematical Society, vol. 145, no. 6. American Mathematical Society, pp. 2441–2454, 2017. ista: Lewin M, Nam P, Rougerie N. 2017. A note on 2D focusing many boson systems. Proceedings of the American Mathematical Society. 145(6), 2441–2454. mla: Lewin, Mathieu, et al. “A Note on 2D Focusing Many Boson Systems.” Proceedings of the American Mathematical Society, vol. 145, no. 6, American Mathematical Society, 2017, pp. 2441–54, doi:10.1090/proc/13468. short: M. Lewin, P. Nam, N. Rougerie, Proceedings of the American Mathematical Society 145 (2017) 2441–2454. date_created: 2018-12-11T11:47:36Z date_published: 2017-01-01T00:00:00Z date_updated: 2021-01-12T08:07:03Z day: '01' department: - _id: RoSe doi: 10.1090/proc/13468 ec_funded: 1 intvolume: ' 145' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1509.09045 month: '01' oa: 1 oa_version: Submitted Version page: 2441 - 2454 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Proceedings of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '7160' quality_controlled: '1' scopus_import: 1 status: public title: A note on 2D focusing many boson systems type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 145 year: '2017' ... --- _id: '1198' abstract: - lang: eng text: We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles effectively decreases the interaction strength. We show that the model becomes trivial in the thermodynamic limit, in the sense that the free energy density at any given particle density and temperature agrees with the corresponding expression for non-interacting particles. acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_processing_charge: Yes (via OA deal) author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Triviality of a model of particles with point interactions in the thermodynamic limit. Letters in Mathematical Physics. 2017;107(3):533-552. doi:10.1007/s11005-016-0915-x apa: Moser, T., & Seiringer, R. (2017). Triviality of a model of particles with point interactions in the thermodynamic limit. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0915-x chicago: Moser, Thomas, and Robert Seiringer. “Triviality of a Model of Particles with Point Interactions in the Thermodynamic Limit.” Letters in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s11005-016-0915-x. ieee: T. Moser and R. Seiringer, “Triviality of a model of particles with point interactions in the thermodynamic limit,” Letters in Mathematical Physics, vol. 107, no. 3. Springer, pp. 533–552, 2017. ista: Moser T, Seiringer R. 2017. Triviality of a model of particles with point interactions in the thermodynamic limit. Letters in Mathematical Physics. 107(3), 533–552. mla: Moser, Thomas, and Robert Seiringer. “Triviality of a Model of Particles with Point Interactions in the Thermodynamic Limit.” Letters in Mathematical Physics, vol. 107, no. 3, Springer, 2017, pp. 533–52, doi:10.1007/s11005-016-0915-x. short: T. Moser, R. Seiringer, Letters in Mathematical Physics 107 (2017) 533–552. date_created: 2018-12-11T11:50:40Z date_published: 2017-03-01T00:00:00Z date_updated: 2023-09-20T11:18:13Z day: '01' ddc: - '510' - '539' department: - _id: RoSe doi: 10.1007/s11005-016-0915-x external_id: isi: - '000394280200007' file: - access_level: open_access checksum: c0c835def162c1bc52f978fad26e3c2f content_type: application/pdf creator: system date_created: 2018-12-12T10:17:40Z date_updated: 2020-07-14T12:44:38Z file_id: '5296' file_name: IST-2016-723-v1+1_s11005-016-0915-x.pdf file_size: 587207 relation: main_file file_date_updated: 2020-07-14T12:44:38Z has_accepted_license: '1' intvolume: ' 107' isi: 1 issue: '3' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: ' 533 - 552' project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Letters in Mathematical Physics publication_identifier: issn: - '03779017' publication_status: published publisher: Springer publist_id: '6152' pubrep_id: '723' quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Triviality of a model of particles with point interactions in the thermodynamic limit tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 107 year: '2017' ... --- _id: '1120' abstract: - lang: eng text: 'The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of the symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates. ' article_number: '033608' article_processing_charge: No author: - first_name: Xiang full_name: Li, Xiang id: 4B7E523C-F248-11E8-B48F-1D18A9856A87 last_name: Li - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 citation: ama: Li X, Seiringer R, Lemeshko M. Angular self-localization of impurities rotating in a bosonic bath. Physical Review A. 2017;95(3). doi:10.1103/PhysRevA.95.033608 apa: Li, X., Seiringer, R., & Lemeshko, M. (2017). Angular self-localization of impurities rotating in a bosonic bath. Physical Review A. American Physical Society. https://doi.org/10.1103/PhysRevA.95.033608 chicago: Li, Xiang, Robert Seiringer, and Mikhail Lemeshko. “Angular Self-Localization of Impurities Rotating in a Bosonic Bath.” Physical Review A. American Physical Society, 2017. https://doi.org/10.1103/PhysRevA.95.033608. ieee: X. Li, R. Seiringer, and M. Lemeshko, “Angular self-localization of impurities rotating in a bosonic bath,” Physical Review A, vol. 95, no. 3. American Physical Society, 2017. ista: Li X, Seiringer R, Lemeshko M. 2017. Angular self-localization of impurities rotating in a bosonic bath. Physical Review A. 95(3), 033608. mla: Li, Xiang, et al. “Angular Self-Localization of Impurities Rotating in a Bosonic Bath.” Physical Review A, vol. 95, no. 3, 033608, American Physical Society, 2017, doi:10.1103/PhysRevA.95.033608. short: X. Li, R. Seiringer, M. Lemeshko, Physical Review A 95 (2017). date_created: 2018-12-11T11:50:15Z date_published: 2017-03-06T00:00:00Z date_updated: 2023-09-20T11:30:58Z day: '06' department: - _id: MiLe - _id: RoSe doi: 10.1103/PhysRevA.95.033608 ec_funded: 1 external_id: isi: - '000395981900009' intvolume: ' 95' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1610.04908 month: '03' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: 26031614-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P29902 name: Quantum rotations in the presence of a many-body environment publication: Physical Review A publication_identifier: issn: - '24699926' publication_status: published publisher: American Physical Society publist_id: '6242' quality_controlled: '1' related_material: record: - id: '8958' relation: dissertation_contains status: public scopus_import: '1' status: public title: Angular self-localization of impurities rotating in a bosonic bath type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 95 year: '2017' ... --- _id: '1079' abstract: - lang: eng text: We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers. article_number: '6' article_processing_charge: No author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Hanne full_name: Van Den Bosch, Hanne last_name: Van Den Bosch citation: ama: Nam P, Van Den Bosch H. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 2017;20(2). doi:10.1007/s11040-017-9238-0 apa: Nam, P., & Van Den Bosch, H. (2017). Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-017-9238-0 chicago: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry. Springer, 2017. https://doi.org/10.1007/s11040-017-9238-0. ieee: P. Nam and H. Van Den Bosch, “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges,” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2. Springer, 2017. ista: Nam P, Van Den Bosch H. 2017. Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges. Mathematical Physics, Analysis and Geometry. 20(2), 6. mla: Nam, Phan, and Hanne Van Den Bosch. “Nonexistence in Thomas Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges.” Mathematical Physics, Analysis and Geometry, vol. 20, no. 2, 6, Springer, 2017, doi:10.1007/s11040-017-9238-0. short: P. Nam, H. Van Den Bosch, Mathematical Physics, Analysis and Geometry 20 (2017). date_created: 2018-12-11T11:50:02Z date_published: 2017-06-01T00:00:00Z date_updated: 2023-09-20T11:53:35Z day: '01' department: - _id: RoSe doi: 10.1007/s11040-017-9238-0 external_id: isi: - '000401270000004' intvolume: ' 20' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1603.07368 month: '06' oa: 1 oa_version: Submitted Version project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Mathematical Physics, Analysis and Geometry publication_identifier: issn: - '13850172' publication_status: published publisher: Springer publist_id: '6300' quality_controlled: '1' scopus_import: '1' status: public title: Nonexistence in Thomas Fermi-Dirac-von Weizsäcker theory with small nuclear charges type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 20 year: '2017' ... --- _id: '741' abstract: - lang: eng text: We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain. article_processing_charge: No author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 2017;356(1):329-355. doi:10.1007/s00220-017-2980-0 apa: Moser, T., & Seiringer, R. (2017). Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-017-2980-0 chicago: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-017-2980-0. ieee: T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with point interactions,” Communications in Mathematical Physics, vol. 356, no. 1. Springer, pp. 329–355, 2017. ista: Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 356(1), 329–355. mla: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” Communications in Mathematical Physics, vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:10.1007/s00220-017-2980-0. short: T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017) 329–355. date_created: 2018-12-11T11:48:15Z date_published: 2017-11-01T00:00:00Z date_updated: 2023-09-27T12:34:15Z day: '01' ddc: - '539' department: - _id: RoSe doi: 10.1007/s00220-017-2980-0 ec_funded: 1 external_id: isi: - '000409821300010' file: - access_level: open_access checksum: 0fd9435400f91e9b3c5346319a2d24e3 content_type: application/pdf creator: system date_created: 2018-12-12T10:10:50Z date_updated: 2020-07-14T12:47:57Z file_id: '4841' file_name: IST-2017-880-v1+1_s00220-017-2980-0.pdf file_size: 952639 relation: main_file file_date_updated: 2020-07-14T12:47:57Z has_accepted_license: '1' intvolume: ' 356' isi: 1 issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 329 - 355 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Communications in Mathematical Physics publication_identifier: issn: - '00103616' publication_status: published publisher: Springer publist_id: '6926' pubrep_id: '880' quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Stability of a fermionic N+1 particle system with point interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 356 year: '2017' ... --- _id: '739' abstract: - lang: eng text: We study the norm approximation to the Schrödinger dynamics of N bosons in with an interaction potential of the form . Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large N limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all . The range of β is expected to be optimal for this large class of initial states. article_processing_charge: No author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski citation: ama: Nam P, Napiórkowski MM. A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 2017;108(5):662-688. doi:10.1016/j.matpur.2017.05.013 apa: Nam, P., & Napiórkowski, M. M. (2017). A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. Elsevier. https://doi.org/10.1016/j.matpur.2017.05.013 chicago: Nam, Phan, and Marcin M Napiórkowski. “A Note on the Validity of Bogoliubov Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées. Elsevier, 2017. https://doi.org/10.1016/j.matpur.2017.05.013. ieee: P. Nam and M. M. Napiórkowski, “A note on the validity of Bogoliubov correction to mean field dynamics,” Journal de Mathématiques Pures et Appliquées, vol. 108, no. 5. Elsevier, pp. 662–688, 2017. ista: Nam P, Napiórkowski MM. 2017. A note on the validity of Bogoliubov correction to mean field dynamics. Journal de Mathématiques Pures et Appliquées. 108(5), 662–688. mla: Nam, Phan, and Marcin M. Napiórkowski. “A Note on the Validity of Bogoliubov Correction to Mean Field Dynamics.” Journal de Mathématiques Pures et Appliquées, vol. 108, no. 5, Elsevier, 2017, pp. 662–88, doi:10.1016/j.matpur.2017.05.013. short: P. Nam, M.M. Napiórkowski, Journal de Mathématiques Pures et Appliquées 108 (2017) 662–688. date_created: 2018-12-11T11:48:15Z date_published: 2017-11-01T00:00:00Z date_updated: 2023-09-27T12:52:07Z day: '01' department: - _id: RoSe doi: 10.1016/j.matpur.2017.05.013 external_id: isi: - '000414113600003' intvolume: ' 108' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1604.05240 month: '11' oa: 1 oa_version: Submitted Version page: 662 - 688 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Journal de Mathématiques Pures et Appliquées publication_identifier: issn: - '00217824' publication_status: published publisher: Elsevier publist_id: '6928' quality_controlled: '1' scopus_import: '1' status: public title: A note on the validity of Bogoliubov correction to mean field dynamics type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 108 year: '2017' ... --- _id: '997' abstract: - lang: eng text: Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems. article_number: '235301' article_processing_charge: No article_type: original author: - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 citation: ama: Yakaboylu E, Deuchert A, Lemeshko M. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. Physical Review Letters. 2017;119(23). doi:10.1103/PhysRevLett.119.235301 apa: Yakaboylu, E., Deuchert, A., & Lemeshko, M. (2017). Emergence of non-abelian magnetic monopoles in a quantum impurity problem. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.119.235301 chicago: Yakaboylu, Enderalp, Andreas Deuchert, and Mikhail Lemeshko. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” Physical Review Letters. American Physical Society, 2017. https://doi.org/10.1103/PhysRevLett.119.235301. ieee: E. Yakaboylu, A. Deuchert, and M. Lemeshko, “Emergence of non-abelian magnetic monopoles in a quantum impurity problem,” Physical Review Letters, vol. 119, no. 23. American Physical Society, 2017. ista: Yakaboylu E, Deuchert A, Lemeshko M. 2017. Emergence of non-abelian magnetic monopoles in a quantum impurity problem. Physical Review Letters. 119(23), 235301. mla: Yakaboylu, Enderalp, et al. “Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem.” Physical Review Letters, vol. 119, no. 23, 235301, American Physical Society, 2017, doi:10.1103/PhysRevLett.119.235301. short: E. Yakaboylu, A. Deuchert, M. Lemeshko, Physical Review Letters 119 (2017). date_created: 2018-12-11T11:49:36Z date_published: 2017-12-06T00:00:00Z date_updated: 2023-10-10T13:31:54Z day: '06' department: - _id: MiLe - _id: RoSe doi: 10.1103/PhysRevLett.119.235301 ec_funded: 1 external_id: arxiv: - '1705.05162' isi: - '000417132100007' intvolume: ' 119' isi: 1 issue: '23' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.05162 month: '12' oa: 1 oa_version: Preprint project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 26031614-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P29902 name: Quantum rotations in the presence of a many-body environment publication: Physical Review Letters publication_identifier: issn: - 0031-9007 publication_status: published publisher: American Physical Society publist_id: '6401' quality_controlled: '1' scopus_import: '1' status: public title: Emergence of non-abelian magnetic monopoles in a quantum impurity problem type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 119 year: '2017' ... --- _id: '912' abstract: - lang: eng text: "We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.\r\n" article_number: '081901' article_processing_charge: No author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 citation: ama: Deuchert A. A lower bound for the BCS functional with boundary conditions at infinity. Journal of Mathematical Physics. 2017;58(8). doi:10.1063/1.4996580 apa: Deuchert, A. (2017). A lower bound for the BCS functional with boundary conditions at infinity. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/1.4996580 chicago: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” Journal of Mathematical Physics. AIP Publishing, 2017. https://doi.org/10.1063/1.4996580. ieee: A. Deuchert, “A lower bound for the BCS functional with boundary conditions at infinity,” Journal of Mathematical Physics, vol. 58, no. 8. AIP Publishing, 2017. ista: Deuchert A. 2017. A lower bound for the BCS functional with boundary conditions at infinity. Journal of Mathematical Physics. 58(8), 081901. mla: Deuchert, Andreas. “A Lower Bound for the BCS Functional with Boundary Conditions at Infinity.” Journal of Mathematical Physics, vol. 58, no. 8, 081901, AIP Publishing, 2017, doi:10.1063/1.4996580. short: A. Deuchert, Journal of Mathematical Physics 58 (2017). date_created: 2018-12-11T11:49:10Z date_published: 2017-08-01T00:00:00Z date_updated: 2024-02-28T13:07:56Z day: '01' department: - _id: RoSe doi: 10.1063/1.4996580 ec_funded: 1 external_id: isi: - '000409197200015' intvolume: ' 58' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1703.04616 month: '08' oa: 1 oa_version: Submitted Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: ' Journal of Mathematical Physics' publication_identifier: issn: - '00222488' publication_status: published publisher: AIP Publishing publist_id: '6531' quality_controlled: '1' scopus_import: '1' status: public title: A lower bound for the BCS functional with boundary conditions at infinity type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 58 year: '2017' ... --- _id: '1143' abstract: - lang: eng text: We study the ground state of a dilute Bose gas in a scaling limit where the Gross-Pitaevskii functional emerges. This is a repulsive nonlinear Schrödinger functional whose quartic term is proportional to the scattering length of the interparticle interaction potential. We propose a new derivation of this limit problem, with a method that bypasses some of the technical difficulties that previous derivations had to face. The new method is based on a combination of Dyson\'s lemma, the quantum de Finetti theorem and a second moment estimate for ground states of the effective Dyson Hamiltonian. It applies equally well to the case where magnetic fields or rotation are present. author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Nicolas full_name: Rougerie, Nicolas last_name: Rougerie - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Nam P, Rougerie N, Seiringer R. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 2016;9(2):459-485. doi:10.2140/apde.2016.9.459' apa: 'Nam, P., Rougerie, N., & Seiringer, R. (2016). Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/apde.2016.9.459' chicago: 'Nam, Phan, Nicolas Rougerie, and Robert Seiringer. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE. Mathematical Sciences Publishers, 2016. https://doi.org/10.2140/apde.2016.9.459.' ieee: 'P. Nam, N. Rougerie, and R. Seiringer, “Ground states of large bosonic systems: The gross Pitaevskii limit revisited,” Analysis and PDE, vol. 9, no. 2. Mathematical Sciences Publishers, pp. 459–485, 2016.' ista: 'Nam P, Rougerie N, Seiringer R. 2016. Ground states of large bosonic systems: The gross Pitaevskii limit revisited. Analysis and PDE. 9(2), 459–485.' mla: 'Nam, Phan, et al. “Ground States of Large Bosonic Systems: The Gross Pitaevskii Limit Revisited.” Analysis and PDE, vol. 9, no. 2, Mathematical Sciences Publishers, 2016, pp. 459–85, doi:10.2140/apde.2016.9.459.' short: P. Nam, N. Rougerie, R. Seiringer, Analysis and PDE 9 (2016) 459–485. date_created: 2018-12-11T11:50:23Z date_published: 2016-03-24T00:00:00Z date_updated: 2021-01-12T06:48:36Z day: '24' department: - _id: RoSe doi: 10.2140/apde.2016.9.459 ec_funded: 1 intvolume: ' 9' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1503.07061 month: '03' oa: 1 oa_version: Preprint page: 459 - 485 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Analysis and PDE publication_status: published publisher: Mathematical Sciences Publishers publist_id: '6215' quality_controlled: '1' scopus_import: 1 status: public title: 'Ground states of large bosonic systems: The gross Pitaevskii limit revisited' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2016' ... --- _id: '1259' abstract: - lang: eng text: We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional. acknowledgement: Partial financial support from the DFG grant GRK 1838, as well as the Austrian Science Fund (FWF), project Nr. P 27533-N27 (R.S.), is gratefully acknowledged. article_number: '13' article_processing_charge: Yes (via OA deal) author: - first_name: Gerhard full_name: Bräunlich, Gerhard last_name: Bräunlich - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Bräunlich G, Hainzl C, Seiringer R. Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. Mathematical Physics, Analysis and Geometry. 2016;19(2). doi:10.1007/s11040-016-9209-x apa: Bräunlich, G., Hainzl, C., & Seiringer, R. (2016). Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-016-9209-x chicago: Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit.” Mathematical Physics, Analysis and Geometry. Springer, 2016. https://doi.org/10.1007/s11040-016-9209-x. ieee: G. Bräunlich, C. Hainzl, and R. Seiringer, “Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit,” Mathematical Physics, Analysis and Geometry, vol. 19, no. 2. Springer, 2016. ista: Bräunlich G, Hainzl C, Seiringer R. 2016. Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit. Mathematical Physics, Analysis and Geometry. 19(2), 13. mla: Bräunlich, Gerhard, et al. “Bogolubov–Hartree–Fock Theory for Strongly Interacting Fermions in the Low Density Limit.” Mathematical Physics, Analysis and Geometry, vol. 19, no. 2, 13, Springer, 2016, doi:10.1007/s11040-016-9209-x. short: G. Bräunlich, C. Hainzl, R. Seiringer, Mathematical Physics, Analysis and Geometry 19 (2016). date_created: 2018-12-11T11:50:59Z date_published: 2016-06-01T00:00:00Z date_updated: 2021-01-12T06:49:27Z day: '01' ddc: - '510' - '539' department: - _id: RoSe doi: 10.1007/s11040-016-9209-x file: - access_level: open_access checksum: 9954f685cc25c58d7f1712c67b47ad8d content_type: application/pdf creator: system date_created: 2018-12-12T10:09:13Z date_updated: 2020-07-14T12:44:42Z file_id: '4736' file_name: IST-2016-702-v1+1_s11040-016-9209-x.pdf file_size: 506242 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 19' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Mathematical Physics, Analysis and Geometry publication_status: published publisher: Springer publist_id: '6066' pubrep_id: '702' quality_controlled: '1' scopus_import: 1 status: public title: Bogolubov–Hartree–Fock theory for strongly interacting fermions in the low density limit tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2016' ... --- _id: '1267' abstract: - lang: eng text: We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result. acknowledgement: "Open access funding provided by Institute of Science and Technology Austria.\r\n" author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Rowan full_name: Killip, Rowan last_name: Killip - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam citation: ama: Frank R, Killip R, Nam P. Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. 2016;106(8):1033-1036. doi:10.1007/s11005-016-0860-8 apa: Frank, R., Killip, R., & Nam, P. (2016). Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0860-8 chicago: Frank, Rupert, Rowan Killip, and Phan Nam. “Nonexistence of Large Nuclei in the Liquid Drop Model.” Letters in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s11005-016-0860-8. ieee: R. Frank, R. Killip, and P. Nam, “Nonexistence of large nuclei in the liquid drop model,” Letters in Mathematical Physics, vol. 106, no. 8. Springer, pp. 1033–1036, 2016. ista: Frank R, Killip R, Nam P. 2016. Nonexistence of large nuclei in the liquid drop model. Letters in Mathematical Physics. 106(8), 1033–1036. mla: Frank, Rupert, et al. “Nonexistence of Large Nuclei in the Liquid Drop Model.” Letters in Mathematical Physics, vol. 106, no. 8, Springer, 2016, pp. 1033–36, doi:10.1007/s11005-016-0860-8. short: R. Frank, R. Killip, P. Nam, Letters in Mathematical Physics 106 (2016) 1033–1036. date_created: 2018-12-11T11:51:02Z date_published: 2016-08-01T00:00:00Z date_updated: 2021-01-12T06:49:30Z day: '01' ddc: - '510' - '539' department: - _id: RoSe doi: 10.1007/s11005-016-0860-8 file: - access_level: open_access checksum: d740a6a226e0f5f864f40e3e269d3cc0 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:09Z date_updated: 2020-07-14T12:44:42Z file_id: '4863' file_name: IST-2016-698-v1+1_s11005-016-0860-8.pdf file_size: 349464 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 106' issue: '8' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 1033 - 1036 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '6054' pubrep_id: '698' quality_controlled: '1' scopus_import: 1 status: public title: Nonexistence of large nuclei in the liquid drop model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 106 year: '2016' ... --- _id: '1291' abstract: - lang: eng text: We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity. acknowledgement: "Open access funding provided by Institute of Science and Technology (IST Austria). The\r\nresearch leading to these results has received funding from the European Research Council under the European\r\nUnion’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694), from\r\nthe Italian PRIN National Grant Geometric and analytic theory of Hamiltonian systems in finite and infinite\r\ndimensions, and the Austrian Science Fund (FWF), project Nr. P 27533-N27. Part of this work was completed\r\nduring a stay at the Erwin Schrödinger Institute for Mathematical Physics in Vienna (ESI program 2015\r\n“Quantum many-body systems, random matrices, and disorder”), whose hospitality and financial support is\r\ngratefully acknowledged." author: - first_name: Alessandro full_name: Giuliani, Alessandro last_name: Giuliani - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Giuliani A, Seiringer R. Periodic striped ground states in Ising models with competing interactions. Communications in Mathematical Physics. 2016;347(3):983-1007. doi:10.1007/s00220-016-2665-0 apa: Giuliani, A., & Seiringer, R. (2016). Periodic striped ground states in Ising models with competing interactions. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2665-0 chicago: Giuliani, Alessandro, and Robert Seiringer. “Periodic Striped Ground States in Ising Models with Competing Interactions.” Communications in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-016-2665-0. ieee: A. Giuliani and R. Seiringer, “Periodic striped ground states in Ising models with competing interactions,” Communications in Mathematical Physics, vol. 347, no. 3. Springer, pp. 983–1007, 2016. ista: Giuliani A, Seiringer R. 2016. Periodic striped ground states in Ising models with competing interactions. Communications in Mathematical Physics. 347(3), 983–1007. mla: Giuliani, Alessandro, and Robert Seiringer. “Periodic Striped Ground States in Ising Models with Competing Interactions.” Communications in Mathematical Physics, vol. 347, no. 3, Springer, 2016, pp. 983–1007, doi:10.1007/s00220-016-2665-0. short: A. Giuliani, R. Seiringer, Communications in Mathematical Physics 347 (2016) 983–1007. date_created: 2018-12-11T11:51:11Z date_published: 2016-11-01T00:00:00Z date_updated: 2021-01-12T06:49:40Z day: '01' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1007/s00220-016-2665-0 file: - access_level: open_access checksum: 3c6e08c048fc462e312788be72874bb1 content_type: application/pdf creator: system date_created: 2018-12-12T10:09:02Z date_updated: 2020-07-14T12:44:42Z file_id: '4725' file_name: IST-2016-688-v1+1_s00220-016-2665-0.pdf file_size: 794983 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 347' issue: '3' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 983 - 1007 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '6025' pubrep_id: '688' quality_controlled: '1' scopus_import: 1 status: public title: Periodic striped ground states in Ising models with competing interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 347 year: '2016' ... --- _id: '1428' abstract: - lang: eng text: We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential. article_number: '012016' author: - first_name: Martin full_name: Könenberg, Martin last_name: Könenberg - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: 'Könenberg M, Moser T, Seiringer R, Yngvason J. Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. In: Journal of Physics: Conference Series. Vol 691. IOP Publishing Ltd.; 2016. doi:10.1088/1742-6596/691/1/012016' apa: 'Könenberg, M., Moser, T., Seiringer, R., & Yngvason, J. (2016). Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. In Journal of Physics: Conference Series (Vol. 691). Shanghai, China: IOP Publishing Ltd. https://doi.org/10.1088/1742-6596/691/1/012016' chicago: 'Könenberg, Martin, Thomas Moser, Robert Seiringer, and Jakob Yngvason. “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential.” In Journal of Physics: Conference Series, Vol. 691. IOP Publishing Ltd., 2016. https://doi.org/10.1088/1742-6596/691/1/012016.' ieee: 'M. Könenberg, T. Moser, R. Seiringer, and J. Yngvason, “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential,” in Journal of Physics: Conference Series, Shanghai, China, 2016, vol. 691, no. 1.' ista: 'Könenberg M, Moser T, Seiringer R, Yngvason J. 2016. Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential. Journal of Physics: Conference Series. 24th International Laser Physics Workshop (LPHYS’15) vol. 691, 012016.' mla: 'Könenberg, Martin, et al. “Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential.” Journal of Physics: Conference Series, vol. 691, no. 1, 012016, IOP Publishing Ltd., 2016, doi:10.1088/1742-6596/691/1/012016.' short: 'M. Könenberg, T. Moser, R. Seiringer, J. Yngvason, in:, Journal of Physics: Conference Series, IOP Publishing Ltd., 2016.' conference: end_date: 2015-08-25 location: Shanghai, China name: 24th International Laser Physics Workshop (LPHYS'15) start_date: 2015-08-21 date_created: 2018-12-11T11:51:58Z date_published: 2016-03-07T00:00:00Z date_updated: 2021-01-12T06:50:40Z day: '07' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1088/1742-6596/691/1/012016 file: - access_level: open_access checksum: 109db801749072c3f6c8f1a1848700fa content_type: application/pdf creator: system date_created: 2018-12-12T10:10:55Z date_updated: 2020-07-14T12:44:53Z file_id: '4847' file_name: IST-2016-585-v1+1_JPCS_691_1_012016.pdf file_size: 1434688 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 691' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: 'Journal of Physics: Conference Series' publication_status: published publisher: IOP Publishing Ltd. publist_id: '5770' pubrep_id: '585' quality_controlled: '1' scopus_import: 1 status: public title: Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 691 year: '2016' ... --- _id: '1422' abstract: - lang: eng text: We study the time-dependent Bogoliubov–de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg–Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior. acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_processing_charge: Yes (via OA deal) author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Hainzl C, Schlein B, Seiringer R. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 2016;106(7):913-923. doi:10.1007/s11005-016-0847-5 apa: Frank, R., Hainzl, C., Schlein, B., & Seiringer, R. (2016). Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-016-0847-5 chicago: Frank, Rupert, Christian Hainzl, Benjamin Schlein, and Robert Seiringer. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” Letters in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s11005-016-0847-5. ieee: R. Frank, C. Hainzl, B. Schlein, and R. Seiringer, “Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations,” Letters in Mathematical Physics, vol. 106, no. 7. Springer, pp. 913–923, 2016. ista: Frank R, Hainzl C, Schlein B, Seiringer R. 2016. Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations. Letters in Mathematical Physics. 106(7), 913–923. mla: Frank, Rupert, et al. “Incompatibility of Time-Dependent Bogoliubov–de-Gennes and Ginzburg–Landau Equations.” Letters in Mathematical Physics, vol. 106, no. 7, Springer, 2016, pp. 913–23, doi:10.1007/s11005-016-0847-5. short: R. Frank, C. Hainzl, B. Schlein, R. Seiringer, Letters in Mathematical Physics 106 (2016) 913–923. date_created: 2018-12-11T11:51:56Z date_published: 2016-07-01T00:00:00Z date_updated: 2021-01-12T06:50:38Z day: '01' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1007/s11005-016-0847-5 file: - access_level: open_access checksum: fb404923d8ca9a1faeb949561f26cbea content_type: application/pdf creator: system date_created: 2018-12-12T10:15:57Z date_updated: 2020-07-14T12:44:53Z file_id: '5181' file_name: IST-2016-591-v1+1_s11005-016-0847-5.pdf file_size: 458968 relation: main_file file_date_updated: 2020-07-14T12:44:53Z has_accepted_license: '1' intvolume: ' 106' issue: '7' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 913 - 923 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '5785' pubrep_id: '591' quality_controlled: '1' scopus_import: 1 status: public title: Incompatibility of time-dependent Bogoliubov–de-Gennes and Ginzburg–Landau equations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 106 year: '2016' ... --- _id: '1436' abstract: - lang: eng text: We study the time evolution of a system of N spinless fermions in R3 which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation with the time-dependent Hartree-Fock approximation, and we give an estimate for the accuracy of this approximation in terms of the kinetic energy of the system. This leads, in turn, to bounds in terms of the initial total energy of the system. author: - first_name: Volker full_name: Bach, Volker last_name: Bach - first_name: Sébastien full_name: Breteaux, Sébastien last_name: Breteaux - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 - first_name: Peter full_name: Pickl, Peter last_name: Pickl - first_name: Tim full_name: Tzaneteas, Tim last_name: Tzaneteas citation: ama: Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 2016;105(1):1-30. doi:10.1016/j.matpur.2015.09.003 apa: Bach, V., Breteaux, S., Petrat, S. P., Pickl, P., & Tzaneteas, T. (2016). Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. Elsevier. https://doi.org/10.1016/j.matpur.2015.09.003 chicago: Bach, Volker, Sébastien Breteaux, Sören P Petrat, Peter Pickl, and Tim Tzaneteas. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” Journal de Mathématiques Pures et Appliquées. Elsevier, 2016. https://doi.org/10.1016/j.matpur.2015.09.003. ieee: V. Bach, S. Breteaux, S. P. Petrat, P. Pickl, and T. Tzaneteas, “Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction,” Journal de Mathématiques Pures et Appliquées, vol. 105, no. 1. Elsevier, pp. 1–30, 2016. ista: Bach V, Breteaux S, Petrat SP, Pickl P, Tzaneteas T. 2016. Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction. Journal de Mathématiques Pures et Appliquées. 105(1), 1–30. mla: Bach, Volker, et al. “Kinetic Energy Estimates for the Accuracy of the Time-Dependent Hartree-Fock Approximation with Coulomb Interaction.” Journal de Mathématiques Pures et Appliquées, vol. 105, no. 1, Elsevier, 2016, pp. 1–30, doi:10.1016/j.matpur.2015.09.003. short: V. Bach, S. Breteaux, S.P. Petrat, P. Pickl, T. Tzaneteas, Journal de Mathématiques Pures et Appliquées 105 (2016) 1–30. date_created: 2018-12-11T11:52:00Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:50:43Z day: '01' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1016/j.matpur.2015.09.003 ec_funded: 1 file: - access_level: open_access checksum: c5afe1f6935bc7f2b546adbde1d31a35 content_type: application/pdf creator: system date_created: 2018-12-12T10:10:36Z date_updated: 2020-07-14T12:44:54Z file_id: '4825' file_name: IST-2016-581-v1+1_1-s2.0-S0021782415001191-main.pdf file_size: 658491 relation: main_file file_date_updated: 2020-07-14T12:44:54Z has_accepted_license: '1' intvolume: ' 105' issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-nd/4.0/ month: '01' oa: 1 oa_version: Published Version page: 1 - 30 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal de Mathématiques Pures et Appliquées publication_status: published publisher: Elsevier publist_id: '5763' pubrep_id: '581' quality_controlled: '1' scopus_import: 1 status: public title: Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 105 year: '2016' ... --- _id: '1478' abstract: - lang: eng text: We consider the Tonks-Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose-Einstein condensation and no superfluidity, even at zero temperature. article_number: '035002' author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Simone full_name: Warzel, Simone last_name: Warzel citation: ama: Seiringer R, Warzel S. Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. New Journal of Physics. 2016;18(3). doi:10.1088/1367-2630/18/3/035002 apa: Seiringer, R., & Warzel, S. (2016). Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. New Journal of Physics. IOP Publishing Ltd. https://doi.org/10.1088/1367-2630/18/3/035002 chicago: Seiringer, Robert, and Simone Warzel. “Decay of Correlations and Absence of Superfluidity in the Disordered Tonks-Girardeau Gas.” New Journal of Physics. IOP Publishing Ltd., 2016. https://doi.org/10.1088/1367-2630/18/3/035002. ieee: R. Seiringer and S. Warzel, “Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas,” New Journal of Physics, vol. 18, no. 3. IOP Publishing Ltd., 2016. ista: Seiringer R, Warzel S. 2016. Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas. New Journal of Physics. 18(3), 035002. mla: Seiringer, Robert, and Simone Warzel. “Decay of Correlations and Absence of Superfluidity in the Disordered Tonks-Girardeau Gas.” New Journal of Physics, vol. 18, no. 3, 035002, IOP Publishing Ltd., 2016, doi:10.1088/1367-2630/18/3/035002. short: R. Seiringer, S. Warzel, New Journal of Physics 18 (2016). date_created: 2018-12-11T11:52:15Z date_published: 2016-02-29T00:00:00Z date_updated: 2021-01-12T06:51:01Z day: '29' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1088/1367-2630/18/3/035002 file: - access_level: open_access checksum: 4f959eabc19d2a2f518318a450a4d424 content_type: application/pdf creator: system date_created: 2018-12-12T10:17:22Z date_updated: 2020-07-14T12:44:56Z file_id: '5276' file_name: IST-2016-579-v1+1_njp_18_3_035002.pdf file_size: 965607 relation: main_file file_date_updated: 2020-07-14T12:44:56Z has_accepted_license: '1' intvolume: ' 18' issue: '3' language: - iso: eng month: '02' oa: 1 oa_version: Published Version project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: New Journal of Physics publication_status: published publisher: IOP Publishing Ltd. publist_id: '5716' pubrep_id: '579' quality_controlled: '1' scopus_import: 1 status: public title: Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 18 year: '2016' ... --- _id: '1486' abstract: - lang: eng text: We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime. article_number: '021101' author: - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Hainzl C, Seiringer R. The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. Journal of Mathematical Physics. 2016;57(2). doi:10.1063/1.4941723 apa: Hainzl, C., & Seiringer, R. (2016). The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4941723 chicago: Hainzl, Christian, and Robert Seiringer. “The Bardeen–Cooper–Schrieffer Functional of Superconductivity and Its Mathematical Properties.” Journal of Mathematical Physics. American Institute of Physics, 2016. https://doi.org/10.1063/1.4941723. ieee: C. Hainzl and R. Seiringer, “The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties,” Journal of Mathematical Physics, vol. 57, no. 2. American Institute of Physics, 2016. ista: Hainzl C, Seiringer R. 2016. The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties. Journal of Mathematical Physics. 57(2), 021101. mla: Hainzl, Christian, and Robert Seiringer. “The Bardeen–Cooper–Schrieffer Functional of Superconductivity and Its Mathematical Properties.” Journal of Mathematical Physics, vol. 57, no. 2, 021101, American Institute of Physics, 2016, doi:10.1063/1.4941723. short: C. Hainzl, R. Seiringer, Journal of Mathematical Physics 57 (2016). date_created: 2018-12-11T11:52:18Z date_published: 2016-02-24T00:00:00Z date_updated: 2021-01-12T06:51:04Z day: '24' department: - _id: RoSe doi: 10.1063/1.4941723 intvolume: ' 57' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1511.01995 month: '02' oa: 1 oa_version: Preprint publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '5701' quality_controlled: '1' scopus_import: 1 status: public title: The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 57 year: '2016' ... --- _id: '1493' abstract: - lang: eng text: We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock equations as an effective mean-field dynamics from the microscopic Schrödinger equation for fermionic many-particle systems in quantum mechanics. The method is an adaption of the method used in Pickl (Lett. Math. Phys. 97 (2) 151–164 2011) for bosonic systems to fermionic systems. It is based on a Gronwall type estimate for a suitable measure of distance between the microscopic solution and an antisymmetrized product state. We use this method to treat a new mean-field limit for fermions with long-range interactions in a large volume. Some of our results hold for singular attractive or repulsive interactions. We can also treat Coulomb interaction assuming either a mild singularity cutoff or certain regularity conditions on the solutions to the Hartree(-Fock) equations. In the considered limit, the kinetic and interaction energy are of the same order, while the average force is subleading. For some interactions, we prove that the Hartree(-Fock) dynamics is a more accurate approximation than a simpler dynamics that one would expect from the subleading force. With our method we also treat the mean-field limit coupled to a semiclassical limit, which was discussed in the literature before, and we recover some of the previous results. All results hold for initial data close (but not necessarily equal) to antisymmetrized product states and we always provide explicit rates of convergence. acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_number: '3' article_processing_charge: Yes (via OA deal) author: - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: Petrat SP, Pickl P. A new method and a new scaling for deriving fermionic mean-field dynamics. Mathematical Physics, Analysis and Geometry. 2016;19(1). doi:10.1007/s11040-016-9204-2 apa: Petrat, S. P., & Pickl, P. (2016). A new method and a new scaling for deriving fermionic mean-field dynamics. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-016-9204-2 chicago: Petrat, Sören P, and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” Mathematical Physics, Analysis and Geometry. Springer, 2016. https://doi.org/10.1007/s11040-016-9204-2. ieee: S. P. Petrat and P. Pickl, “A new method and a new scaling for deriving fermionic mean-field dynamics,” Mathematical Physics, Analysis and Geometry, vol. 19, no. 1. Springer, 2016. ista: Petrat SP, Pickl P. 2016. A new method and a new scaling for deriving fermionic mean-field dynamics. Mathematical Physics, Analysis and Geometry. 19(1), 3. mla: Petrat, Sören P., and Peter Pickl. “A New Method and a New Scaling for Deriving Fermionic Mean-Field Dynamics.” Mathematical Physics, Analysis and Geometry, vol. 19, no. 1, 3, Springer, 2016, doi:10.1007/s11040-016-9204-2. short: S.P. Petrat, P. Pickl, Mathematical Physics, Analysis and Geometry 19 (2016). date_created: 2018-12-11T11:52:20Z date_published: 2016-03-01T00:00:00Z date_updated: 2021-01-12T06:51:08Z day: '01' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1007/s11040-016-9204-2 ec_funded: 1 file: - access_level: open_access checksum: eb5d2145ef0d377c4f78bf06e18f4529 content_type: application/pdf creator: system date_created: 2018-12-12T10:16:55Z date_updated: 2020-07-14T12:44:58Z file_id: '5246' file_name: IST-2016-514-v1+1_s11040-016-9204-2.pdf file_size: 911310 relation: main_file file_date_updated: 2020-07-14T12:44:58Z has_accepted_license: '1' intvolume: ' 19' issue: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Mathematical Physics, Analysis and Geometry publication_status: published publisher: Springer publist_id: '5690' pubrep_id: '514' quality_controlled: '1' scopus_import: 1 status: public title: A new method and a new scaling for deriving fermionic mean-field dynamics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2016' ... --- _id: '1491' abstract: - lang: eng text: We study the ground state of a trapped Bose gas, starting from the full many-body Schrödinger Hamiltonian, and derive the non-linear Schrödinger energy functional in the limit of a large particle number, when the interaction potential converges slowly to a Dirac delta function. Our method is based on quantitative estimates on the discrepancy between the full many-body energy and its mean-field approximation using Hartree states. These are proved using finite dimensional localization and a quantitative version of the quantum de Finetti theorem. Our approach covers the case of attractive interactions in the regime of stability. In particular, our main new result is a derivation of the 2D attractive non-linear Schrödinger ground state. acknowledgement: The authors acknowledge financial support from the European Research Council (FP7/2007-2013 Grant Agreement MNIQS 258023) and the ANR (Mathostaq project, ANR-13-JS01-0005-01). The second and third authors have benefited from the hospitality of the Institute for Mathematical Science of the National University of Singapore. author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Nicolas full_name: Rougerie, Nicolas last_name: Rougerie citation: ama: Lewin M, Nam P, Rougerie N. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 2016;368(9):6131-6157. doi:10.1090/tran/6537 apa: Lewin, M., Nam, P., & Rougerie, N. (2016). The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/6537 chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society. American Mathematical Society, 2016. https://doi.org/10.1090/tran/6537. ieee: M. Lewin, P. Nam, and N. Rougerie, “The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases,” Transactions of the American Mathematical Society, vol. 368, no. 9. American Mathematical Society, pp. 6131–6157, 2016. ista: Lewin M, Nam P, Rougerie N. 2016. The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases. Transactions of the American Mathematical Society. 368(9), 6131–6157. mla: Lewin, Mathieu, et al. “The Mean-Field Approximation and the Non-Linear Schrödinger Functional for Trapped Bose Gases.” Transactions of the American Mathematical Society, vol. 368, no. 9, American Mathematical Society, 2016, pp. 6131–57, doi:10.1090/tran/6537. short: M. Lewin, P. Nam, N. Rougerie, Transactions of the American Mathematical Society 368 (2016) 6131–6157. date_created: 2018-12-11T11:52:20Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:51:07Z day: '01' department: - _id: RoSe doi: 10.1090/tran/6537 intvolume: ' 368' issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1405.3220 month: '01' oa: 1 oa_version: Submitted Version page: 6131 - 6157 publication: Transactions of the American Mathematical Society publication_status: published publisher: American Mathematical Society publist_id: '5692' quality_controlled: '1' scopus_import: 1 status: public title: The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 368 year: '2016' ... --- _id: '1545' abstract: - lang: eng text: We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute. acknowledgement: We thank Jan Dereziński for several inspiring discussions and useful remarks. We thank the referee for helpful comments. J.P.S. thanks the Erwin Schrödinger Institute for the hospitality during the thematic programme “Quantum many-body systems, random matrices, and disorder”. We gratefully acknowledge the financial supports by the European Union's Seventh Framework Programme under the ERC Advanced Grant ERC-2012-AdG 321029 (J.P.S.) and the REA grant agreement No. 291734 (P.T.N.), as well as the support of the National Science Center (NCN) grant No. 2012/07/N/ST1/03185 and the Austrian Science Fund (FWF) project No. P 27533-N27 (M.N.). author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: Nam P, Napiórkowski MM, Solovej J. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 2016;270(11):4340-4368. doi:10.1016/j.jfa.2015.12.007 apa: Nam, P., Napiórkowski, M. M., & Solovej, J. (2016). Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2015.12.007 chicago: Nam, Phan, Marcin M Napiórkowski, and Jan Solovej. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2015.12.007. ieee: P. Nam, M. M. Napiórkowski, and J. Solovej, “Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations,” Journal of Functional Analysis, vol. 270, no. 11. Academic Press, pp. 4340–4368, 2016. ista: Nam P, Napiórkowski MM, Solovej J. 2016. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations. Journal of Functional Analysis. 270(11), 4340–4368. mla: Nam, Phan, et al. “Diagonalization of Bosonic Quadratic Hamiltonians by Bogoliubov Transformations.” Journal of Functional Analysis, vol. 270, no. 11, Academic Press, 2016, pp. 4340–68, doi:10.1016/j.jfa.2015.12.007. short: P. Nam, M.M. Napiórkowski, J. Solovej, Journal of Functional Analysis 270 (2016) 4340–4368. date_created: 2018-12-11T11:52:38Z date_published: 2016-06-01T00:00:00Z date_updated: 2021-01-12T06:51:30Z day: '01' department: - _id: RoSe doi: 10.1016/j.jfa.2015.12.007 ec_funded: 1 intvolume: ' 270' issue: '11' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.07321 month: '06' oa: 1 oa_version: Submitted Version page: 4340 - 4368 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Journal of Functional Analysis publication_status: published publisher: Academic Press publist_id: '5626' quality_controlled: '1' scopus_import: 1 status: public title: Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 270 year: '2016' ... --- _id: '1620' abstract: - lang: eng text: We consider the Bardeen–Cooper–Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg–Landau equation. acknowledgement: The authors are grateful to I. M. Sigal for useful discussions. Financial support from the US National Science Foundation through Grants PHY-1347399 and DMS-1363432 (R.L.F.), from the Danish council for independent research and from ERC Advanced Grant 321029 (J.P.S.) is acknowledged. author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: Frank R, Hainzl C, Seiringer R, Solovej J. The external field dependence of the BCS critical temperature. Communications in Mathematical Physics. 2016;342(1):189-216. doi:10.1007/s00220-015-2526-2 apa: Frank, R., Hainzl, C., Seiringer, R., & Solovej, J. (2016). The external field dependence of the BCS critical temperature. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-015-2526-2 chicago: Frank, Rupert, Christian Hainzl, Robert Seiringer, and Jan Solovej. “The External Field Dependence of the BCS Critical Temperature.” Communications in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-015-2526-2. ieee: R. Frank, C. Hainzl, R. Seiringer, and J. Solovej, “The external field dependence of the BCS critical temperature,” Communications in Mathematical Physics, vol. 342, no. 1. Springer, pp. 189–216, 2016. ista: Frank R, Hainzl C, Seiringer R, Solovej J. 2016. The external field dependence of the BCS critical temperature. Communications in Mathematical Physics. 342(1), 189–216. mla: Frank, Rupert, et al. “The External Field Dependence of the BCS Critical Temperature.” Communications in Mathematical Physics, vol. 342, no. 1, Springer, 2016, pp. 189–216, doi:10.1007/s00220-015-2526-2. short: R. Frank, C. Hainzl, R. Seiringer, J. Solovej, Communications in Mathematical Physics 342 (2016) 189–216. date_created: 2018-12-11T11:53:04Z date_published: 2016-02-01T00:00:00Z date_updated: 2021-01-12T06:52:03Z day: '01' department: - _id: RoSe doi: 10.1007/s00220-015-2526-2 intvolume: ' 342' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1410.2352 month: '02' oa: 1 oa_version: Submitted Version page: 189 - 216 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '5546' quality_controlled: '1' scopus_import: 1 status: public title: The external field dependence of the BCS critical temperature type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 342 year: '2016' ... --- _id: '1622' abstract: - lang: eng text: We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases. acknowledgement: "We thank Jan Philip Solovej, Robert Seiringer and Vladimir Maz’ya for helpful discussions, as well as Rupert Frank\r\nand the anonymous referee for useful comments. Part of this work has been carried out during a visit at the Institut Mittag-Leffler (Stockholm). D.L. acknowledges financial support by the grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation and the Swedish Research Council grant no. 2013-4734. P.T.N. is supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 291734. F.P. acknowledges support from the ERC project no. 321029 “The\r\nmathematics of the structure of matter”." author: - first_name: Douglas full_name: Lundholm, Douglas last_name: Lundholm - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Fabian full_name: Portmann, Fabian last_name: Portmann citation: ama: Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 2016;219(3):1343-1382. doi:10.1007/s00205-015-0923-5 apa: Lundholm, D., Nam, P., & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-015-0923-5 chicago: Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis. Springer, 2016. https://doi.org/10.1007/s00205-015-0923-5. ieee: D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems,” Archive for Rational Mechanics and Analysis, vol. 219, no. 3. Springer, pp. 1343–1382, 2016. ista: Lundholm D, Nam P, Portmann F. 2016. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 219(3), 1343–1382. mla: Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis, vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:10.1007/s00205-015-0923-5. short: D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382. date_created: 2018-12-11T11:53:05Z date_published: 2016-03-01T00:00:00Z date_updated: 2021-01-12T06:52:04Z day: '01' department: - _id: RoSe doi: 10.1007/s00205-015-0923-5 ec_funded: 1 intvolume: ' 219' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1501.04570 month: '03' oa: 1 oa_version: Submitted Version page: 1343 - 1382 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Archive for Rational Mechanics and Analysis publication_status: published publisher: Springer publist_id: '5542' quality_controlled: '1' scopus_import: 1 status: public title: Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 219 year: '2016' ... --- _id: '1572' abstract: - lang: eng text: "We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neighbor attraction. This attractive interaction makes the lower bound on the free energy particularly tricky: the key idea there is to prove a differential inequality for the two-particle density, which is thereby shown to be smaller than the probability density of a suitably weighted two-particle random process on the lattice.\r\n" author: - first_name: Michele full_name: Correggi, Michele last_name: Correggi - first_name: Alessandro full_name: Giuliani, Alessandro last_name: Giuliani - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Correggi M, Giuliani A, Seiringer R. Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. Communications in Mathematical Physics. 2015;339(1):279-307. doi:10.1007/s00220-015-2402-0 apa: Correggi, M., Giuliani, A., & Seiringer, R. (2015). Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-015-2402-0 chicago: Correggi, Michele, Alessandro Giuliani, and Robert Seiringer. “Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet.” Communications in Mathematical Physics. Springer, 2015. https://doi.org/10.1007/s00220-015-2402-0. ieee: M. Correggi, A. Giuliani, and R. Seiringer, “Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet,” Communications in Mathematical Physics, vol. 339, no. 1. Springer, pp. 279–307, 2015. ista: Correggi M, Giuliani A, Seiringer R. 2015. Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet. Communications in Mathematical Physics. 339(1), 279–307. mla: Correggi, Michele, et al. “Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet.” Communications in Mathematical Physics, vol. 339, no. 1, Springer, 2015, pp. 279–307, doi:10.1007/s00220-015-2402-0. short: M. Correggi, A. Giuliani, R. Seiringer, Communications in Mathematical Physics 339 (2015) 279–307. date_created: 2018-12-11T11:52:47Z date_published: 2015-06-23T00:00:00Z date_updated: 2021-01-12T06:51:41Z day: '23' department: - _id: RoSe doi: 10.1007/s00220-015-2402-0 intvolume: ' 339' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1312.7873 month: '06' oa: 1 oa_version: Preprint page: 279 - 307 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '5599' quality_controlled: '1' scopus_import: 1 status: public title: Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 339 year: '2015' ... --- _id: '1573' abstract: - lang: eng text: We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in ℝ3. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdos, Schlein, and Yau. author: - first_name: Thomas full_name: Chen, Thomas last_name: Chen - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Nataša full_name: Pavlović, Nataša last_name: Pavlović - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Chen T, Hainzl C, Pavlović N, Seiringer R. Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. Communications on Pure and Applied Mathematics. 2015;68(10):1845-1884. doi:10.1002/cpa.21552 apa: Chen, T., Hainzl, C., Pavlović, N., & Seiringer, R. (2015). Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21552 chicago: Chen, Thomas, Christian Hainzl, Nataša Pavlović, and Robert Seiringer. “Unconditional Uniqueness for the Cubic Gross Pitaevskii Hierarchy via Quantum de Finetti.” Communications on Pure and Applied Mathematics. Wiley, 2015. https://doi.org/10.1002/cpa.21552. ieee: T. Chen, C. Hainzl, N. Pavlović, and R. Seiringer, “Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti,” Communications on Pure and Applied Mathematics, vol. 68, no. 10. Wiley, pp. 1845–1884, 2015. ista: Chen T, Hainzl C, Pavlović N, Seiringer R. 2015. Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti. Communications on Pure and Applied Mathematics. 68(10), 1845–1884. mla: Chen, Thomas, et al. “Unconditional Uniqueness for the Cubic Gross Pitaevskii Hierarchy via Quantum de Finetti.” Communications on Pure and Applied Mathematics, vol. 68, no. 10, Wiley, 2015, pp. 1845–84, doi:10.1002/cpa.21552. short: T. Chen, C. Hainzl, N. Pavlović, R. Seiringer, Communications on Pure and Applied Mathematics 68 (2015) 1845–1884. date_created: 2018-12-11T11:52:48Z date_published: 2015-10-01T00:00:00Z date_updated: 2021-01-12T06:51:41Z day: '01' department: - _id: RoSe doi: 10.1002/cpa.21552 intvolume: ' 68' issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1307.3168 month: '10' oa: 1 oa_version: Preprint page: 1845 - 1884 project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: Communications on Pure and Applied Mathematics publication_status: published publisher: Wiley publist_id: '5598' quality_controlled: '1' scopus_import: 1 status: public title: Unconditional uniqueness for the cubic gross pitaevskii hierarchy via quantum de finetti type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 68 year: '2015' ... --- _id: '1704' abstract: - lang: eng text: Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds. author: - first_name: Andreas full_name: Deuchert, Andreas last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Hainzl C, Seiringer R. Note on a family of monotone quantum relative entropies. Letters in Mathematical Physics. 2015;105(10):1449-1466. doi:10.1007/s11005-015-0787-5 apa: Deuchert, A., Hainzl, C., & Seiringer, R. (2015). Note on a family of monotone quantum relative entropies. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-015-0787-5 chicago: Deuchert, Andreas, Christian Hainzl, and Robert Seiringer. “Note on a Family of Monotone Quantum Relative Entropies.” Letters in Mathematical Physics. Springer, 2015. https://doi.org/10.1007/s11005-015-0787-5. ieee: A. Deuchert, C. Hainzl, and R. Seiringer, “Note on a family of monotone quantum relative entropies,” Letters in Mathematical Physics, vol. 105, no. 10. Springer, pp. 1449–1466, 2015. ista: Deuchert A, Hainzl C, Seiringer R. 2015. Note on a family of monotone quantum relative entropies. Letters in Mathematical Physics. 105(10), 1449–1466. mla: Deuchert, Andreas, et al. “Note on a Family of Monotone Quantum Relative Entropies.” Letters in Mathematical Physics, vol. 105, no. 10, Springer, 2015, pp. 1449–66, doi:10.1007/s11005-015-0787-5. short: A. Deuchert, C. Hainzl, R. Seiringer, Letters in Mathematical Physics 105 (2015) 1449–1466. date_created: 2018-12-11T11:53:34Z date_published: 2015-08-05T00:00:00Z date_updated: 2021-01-12T06:52:38Z day: '05' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-015-0787-5 file: - access_level: open_access checksum: fd7307282a314cc1fbbaef77b187516b content_type: application/pdf creator: dernst date_created: 2019-01-15T14:42:07Z date_updated: 2020-07-14T12:45:13Z file_id: '5836' file_name: 2015_LettersMathPhys_Deuchert.pdf file_size: 484967 relation: main_file file_date_updated: 2020-07-14T12:45:13Z has_accepted_license: '1' intvolume: ' 105' issue: '10' language: - iso: eng license: https://creativecommons.org/licenses/by-nc/4.0/ main_file_link: - open_access: '1' url: http://arxiv.org/abs/1502.07205 month: '08' oa: 1 oa_version: Preprint page: 1449 - 1466 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '5432' quality_controlled: '1' scopus_import: 1 status: public title: Note on a family of monotone quantum relative entropies tmp: image: /images/cc_by_nc.png legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) short: CC BY-NC (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 105 year: '2015' ... --- _id: '1807' abstract: - lang: eng text: We study a double Cahn-Hilliard type functional related to the Gross-Pitaevskii energy of two-components Bose-Einstein condensates. In the case of large but same order intercomponent and intracomponent coupling strengths, we prove Γ-convergence to a perimeter minimisation functional with an inhomogeneous surface tension. We study the asymptotic behavior of the surface tension as the ratio between the intercomponent and intracomponent coupling strengths becomes very small or very large and obtain good agreement with the physical literature. We obtain as a consequence, symmetry breaking of the minimisers for the harmonic potential. author: - first_name: Michael full_name: Goldman, Michael last_name: Goldman - first_name: Jimena full_name: Royo-Letelier, Jimena id: 4D3BED28-F248-11E8-B48F-1D18A9856A87 last_name: Royo-Letelier citation: ama: Goldman M, Royo-Letelier J. Sharp interface limit for two components Bose-Einstein condensates. ESAIM - Control, Optimisation and Calculus of Variations. 2015;21(3):603-624. doi:10.1051/cocv/2014040 apa: Goldman, M., & Royo-Letelier, J. (2015). Sharp interface limit for two components Bose-Einstein condensates. ESAIM - Control, Optimisation and Calculus of Variations. EDP Sciences. https://doi.org/10.1051/cocv/2014040 chicago: Goldman, Michael, and Jimena Royo-Letelier. “Sharp Interface Limit for Two Components Bose-Einstein Condensates.” ESAIM - Control, Optimisation and Calculus of Variations. EDP Sciences, 2015. https://doi.org/10.1051/cocv/2014040. ieee: M. Goldman and J. Royo-Letelier, “Sharp interface limit for two components Bose-Einstein condensates,” ESAIM - Control, Optimisation and Calculus of Variations, vol. 21, no. 3. EDP Sciences, pp. 603–624, 2015. ista: Goldman M, Royo-Letelier J. 2015. Sharp interface limit for two components Bose-Einstein condensates. ESAIM - Control, Optimisation and Calculus of Variations. 21(3), 603–624. mla: Goldman, Michael, and Jimena Royo-Letelier. “Sharp Interface Limit for Two Components Bose-Einstein Condensates.” ESAIM - Control, Optimisation and Calculus of Variations, vol. 21, no. 3, EDP Sciences, 2015, pp. 603–24, doi:10.1051/cocv/2014040. short: M. Goldman, J. Royo-Letelier, ESAIM - Control, Optimisation and Calculus of Variations 21 (2015) 603–624. date_created: 2018-12-11T11:54:07Z date_published: 2015-05-01T00:00:00Z date_updated: 2021-01-12T06:53:20Z day: '01' department: - _id: RoSe doi: 10.1051/cocv/2014040 intvolume: ' 21' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1401.1727 month: '05' oa: 1 oa_version: Preprint page: 603 - 624 publication: ESAIM - Control, Optimisation and Calculus of Variations publication_status: published publisher: EDP Sciences publist_id: '5303' quality_controlled: '1' scopus_import: 1 status: public title: Sharp interface limit for two components Bose-Einstein condensates type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2015' ... --- _id: '1880' abstract: - lang: eng text: We investigate the relation between Bose-Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder acknowledgement: Support from the Natural Sciences and Engineering Research Council of Canada NSERC (MK and RS) and from the Austrian Science Fund FWF (JY, under project P 22929-N16) is gratefully acknowledged article_number: '013022' author: - first_name: Martin full_name: Könenberg, Martin last_name: Könenberg - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Könenberg M, Moser T, Seiringer R, Yngvason J. Superfluid behavior of a Bose-Einstein condensate in a random potential. New Journal of Physics. 2015;17. doi:10.1088/1367-2630/17/1/013022 apa: Könenberg, M., Moser, T., Seiringer, R., & Yngvason, J. (2015). Superfluid behavior of a Bose-Einstein condensate in a random potential. New Journal of Physics. IOP Publishing Ltd. https://doi.org/10.1088/1367-2630/17/1/013022 chicago: Könenberg, Martin, Thomas Moser, Robert Seiringer, and Jakob Yngvason. “Superfluid Behavior of a Bose-Einstein Condensate in a Random Potential.” New Journal of Physics. IOP Publishing Ltd., 2015. https://doi.org/10.1088/1367-2630/17/1/013022. ieee: M. Könenberg, T. Moser, R. Seiringer, and J. Yngvason, “Superfluid behavior of a Bose-Einstein condensate in a random potential,” New Journal of Physics, vol. 17. IOP Publishing Ltd., 2015. ista: Könenberg M, Moser T, Seiringer R, Yngvason J. 2015. Superfluid behavior of a Bose-Einstein condensate in a random potential. New Journal of Physics. 17, 013022. mla: Könenberg, Martin, et al. “Superfluid Behavior of a Bose-Einstein Condensate in a Random Potential.” New Journal of Physics, vol. 17, 013022, IOP Publishing Ltd., 2015, doi:10.1088/1367-2630/17/1/013022. short: M. Könenberg, T. Moser, R. Seiringer, J. Yngvason, New Journal of Physics 17 (2015). date_created: 2018-12-11T11:54:30Z date_published: 2015-01-15T00:00:00Z date_updated: 2021-01-12T06:53:48Z day: '15' ddc: - '530' department: - _id: RoSe doi: 10.1088/1367-2630/17/1/013022 file: - access_level: open_access checksum: 38fdf2b5ac30445e26a5d613abd84b16 content_type: application/pdf creator: system date_created: 2018-12-12T10:12:44Z date_updated: 2020-07-14T12:45:20Z file_id: '4963' file_name: IST-2016-447-v1+1_document_1_.pdf file_size: 768108 relation: main_file file_date_updated: 2020-07-14T12:45:20Z has_accepted_license: '1' intvolume: ' 17' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: New Journal of Physics publication_status: published publisher: IOP Publishing Ltd. publist_id: '5214' pubrep_id: '447' quality_controlled: '1' scopus_import: 1 status: public title: Superfluid behavior of a Bose-Einstein condensate in a random potential tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 17 year: '2015' ... --- _id: '2085' abstract: - lang: eng text: 'We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov''s theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov''s theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov''s theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. ' author: - first_name: Phan full_name: Nam, Phan id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Nam - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Nam P, Seiringer R. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 2015;215(2):381-417. doi:10.1007/s00205-014-0781-6 apa: Nam, P., & Seiringer, R. (2015). Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-014-0781-6 chicago: Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis. Springer, 2015. https://doi.org/10.1007/s00205-014-0781-6. ieee: P. Nam and R. Seiringer, “Collective excitations of Bose gases in the mean-field regime,” Archive for Rational Mechanics and Analysis, vol. 215, no. 2. Springer, pp. 381–417, 2015. ista: Nam P, Seiringer R. 2015. Collective excitations of Bose gases in the mean-field regime. Archive for Rational Mechanics and Analysis. 215(2), 381–417. mla: Nam, Phan, and Robert Seiringer. “Collective Excitations of Bose Gases in the Mean-Field Regime.” Archive for Rational Mechanics and Analysis, vol. 215, no. 2, Springer, 2015, pp. 381–417, doi:10.1007/s00205-014-0781-6. short: P. Nam, R. Seiringer, Archive for Rational Mechanics and Analysis 215 (2015) 381–417. date_created: 2018-12-11T11:55:37Z date_published: 2015-02-01T00:00:00Z date_updated: 2021-01-12T06:55:13Z day: '01' department: - _id: RoSe doi: 10.1007/s00205-014-0781-6 intvolume: ' 215' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1402.1153 month: '02' oa: 1 oa_version: Preprint page: 381 - 417 publication: Archive for Rational Mechanics and Analysis publication_status: published publisher: Springer publist_id: '4951' quality_controlled: '1' scopus_import: 1 status: public title: Collective excitations of Bose gases in the mean-field regime type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 215 year: '2015' ... --- _id: '473' abstract: - lang: eng text: We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction strength behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrödinger functional on a finite interval, as well as smoother interactions in dimensions d 2. author: - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Nam full_name: Phan Thanh, Nam id: 404092F4-F248-11E8-B48F-1D18A9856A87 last_name: Phan Thanh - first_name: Nicolas full_name: Rougerie, Nicolas last_name: Rougerie citation: ama: Lewin M, Nam P, Rougerie N. Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2015;2:65-115. doi:10.5802/jep.18 apa: Lewin, M., Nam, P., & Rougerie, N. (2015). Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique. https://doi.org/10.5802/jep.18 chicago: Lewin, Mathieu, Phan Nam, and Nicolas Rougerie. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques. Ecole Polytechnique, 2015. https://doi.org/10.5802/jep.18. ieee: M. Lewin, P. Nam, and N. Rougerie, “Derivation of nonlinear gibbs measures from many-body quantum mechanics,” Journal de l’Ecole Polytechnique - Mathematiques, vol. 2. Ecole Polytechnique, pp. 65–115, 2015. ista: Lewin M, Nam P, Rougerie N. 2015. Derivation of nonlinear gibbs measures from many-body quantum mechanics. Journal de l’Ecole Polytechnique - Mathematiques. 2, 65–115. mla: Lewin, Mathieu, et al. “Derivation of Nonlinear Gibbs Measures from Many-Body Quantum Mechanics.” Journal de l’Ecole Polytechnique - Mathematiques, vol. 2, Ecole Polytechnique, 2015, pp. 65–115, doi:10.5802/jep.18. short: M. Lewin, P. Nam, N. Rougerie, Journal de l’Ecole Polytechnique - Mathematiques 2 (2015) 65–115. date_created: 2018-12-11T11:46:40Z date_published: 2015-01-01T00:00:00Z date_updated: 2021-01-12T08:00:52Z day: '01' ddc: - '539' department: - _id: RoSe doi: 10.5802/jep.18 ec_funded: 1 file: - access_level: open_access checksum: a40eb4016717ddc9927154798a4c164a content_type: application/pdf creator: system date_created: 2018-12-12T10:12:53Z date_updated: 2020-07-14T12:46:35Z file_id: '4974' file_name: IST-2018-951-v1+1_2015_Thanh-Nam_Derivation_of.pdf file_size: 1084254 relation: main_file file_date_updated: 2020-07-14T12:46:35Z has_accepted_license: '1' intvolume: ' 2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 65 - 115 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal de l'Ecole Polytechnique - Mathematiques publication_status: published publisher: Ecole Polytechnique publist_id: '7344' pubrep_id: '951' quality_controlled: '1' scopus_import: 1 status: public title: Derivation of nonlinear gibbs measures from many-body quantum mechanics tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2015' ... --- _id: '1516' abstract: - lang: eng text: "We present a rigorous derivation of the BCS gap equation for superfluid fermionic gases with point interactions. Our starting point is the BCS energy functional, whose minimizer we investigate in the limit when the range of the interaction potential goes to zero.\r\n" article_processing_charge: No author: - first_name: Gerhard full_name: Bräunlich, Gerhard last_name: Bräunlich - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Bräunlich G, Hainzl C, Seiringer R. On the BCS gap equation for superfluid fermionic gases. In: Proceedings of the QMath12 Conference. World Scientific Publishing; 2014:127-137. doi:10.1142/9789814618144_0007' apa: 'Bräunlich, G., Hainzl, C., & Seiringer, R. (2014). On the BCS gap equation for superfluid fermionic gases. In Proceedings of the QMath12 Conference (pp. 127–137). Berlin, Germany: World Scientific Publishing. https://doi.org/10.1142/9789814618144_0007' chicago: Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “On the BCS Gap Equation for Superfluid Fermionic Gases.” In Proceedings of the QMath12 Conference, 127–37. World Scientific Publishing, 2014. https://doi.org/10.1142/9789814618144_0007. ieee: G. Bräunlich, C. Hainzl, and R. Seiringer, “On the BCS gap equation for superfluid fermionic gases,” in Proceedings of the QMath12 Conference, Berlin, Germany, 2014, pp. 127–137. ista: 'Bräunlich G, Hainzl C, Seiringer R. 2014. On the BCS gap equation for superfluid fermionic gases. Proceedings of the QMath12 Conference. QMath: Mathematical Results in Quantum Physics, 127–137.' mla: Bräunlich, Gerhard, et al. “On the BCS Gap Equation for Superfluid Fermionic Gases.” Proceedings of the QMath12 Conference, World Scientific Publishing, 2014, pp. 127–37, doi:10.1142/9789814618144_0007. short: G. Bräunlich, C. Hainzl, R. Seiringer, in:, Proceedings of the QMath12 Conference, World Scientific Publishing, 2014, pp. 127–137. conference: end_date: 2013-09-13 location: Berlin, Germany name: 'QMath: Mathematical Results in Quantum Physics' start_date: 2013-09-10 date_created: 2018-12-11T11:52:28Z date_published: 2014-01-01T00:00:00Z date_updated: 2021-01-12T06:51:19Z day: '01' department: - _id: RoSe doi: 10.1142/9789814618144_0007 external_id: arxiv: - '1403.2563' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1403.2563 month: '01' oa: 1 oa_version: Preprint page: 127 - 137 publication: Proceedings of the QMath12 Conference publication_status: published publisher: World Scientific Publishing publist_id: '5661' quality_controlled: '1' status: public title: On the BCS gap equation for superfluid fermionic gases type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2014' ... --- _id: '1821' abstract: - lang: eng text: We review recent progress towards a rigorous understanding of the Bogoliubov approximation for bosonic quantum many-body systems. We focus, in particular, on the excitation spectrum of a Bose gas in the mean-field (Hartree) limit. A list of open problems will be discussed at the end. article_number: '1.4881536' author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. Journal of Mathematical Physics. 2014;55(7). doi:10.1063/1.4881536 apa: Seiringer, R. (2014). Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4881536 chicago: Seiringer, Robert. “Bose Gases, Bose-Einstein Condensation, and the Bogoliubov Approximation.” Journal of Mathematical Physics. American Institute of Physics, 2014. https://doi.org/10.1063/1.4881536. ieee: R. Seiringer, “Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation,” Journal of Mathematical Physics, vol. 55, no. 7. American Institute of Physics, 2014. ista: Seiringer R. 2014. Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation. Journal of Mathematical Physics. 55(7), 1.4881536. mla: Seiringer, Robert. “Bose Gases, Bose-Einstein Condensation, and the Bogoliubov Approximation.” Journal of Mathematical Physics, vol. 55, no. 7, 1.4881536, American Institute of Physics, 2014, doi:10.1063/1.4881536. short: R. Seiringer, Journal of Mathematical Physics 55 (2014). date_created: 2018-12-11T11:54:11Z date_published: 2014-06-26T00:00:00Z date_updated: 2021-01-12T06:53:25Z day: '26' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1063/1.4881536 file: - access_level: open_access checksum: ed0efc93c10f1341155f0316af617b82 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:49Z date_updated: 2020-07-14T12:45:17Z file_id: '5172' file_name: IST-2016-532-v1+1_J._Mathematical_Phys._2014_Seiringer.pdf file_size: 269171 relation: main_file file_date_updated: 2020-07-14T12:45:17Z has_accepted_license: '1' intvolume: ' 55' issue: '7' language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '5285' pubrep_id: '532' quality_controlled: '1' scopus_import: 1 status: public title: Bose gases, Bose-Einstein condensation, and the Bogoliubov approximation type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2014' ... --- _id: '1822' article_number: '075101' author: - first_name: Vojkan full_name: Jakšić, Vojkan last_name: Jakšić - first_name: Claude full_name: Pillet, Claude last_name: Pillet - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Jakšić V, Pillet C, Seiringer R. Introduction. Journal of Mathematical Physics. 2014;55(7). doi:10.1063/1.4884877 apa: Jakšić, V., Pillet, C., & Seiringer, R. (2014). Introduction. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4884877 chicago: Jakšić, Vojkan, Claude Pillet, and Robert Seiringer. “Introduction.” Journal of Mathematical Physics. American Institute of Physics, 2014. https://doi.org/10.1063/1.4884877. ieee: V. Jakšić, C. Pillet, and R. Seiringer, “Introduction,” Journal of Mathematical Physics, vol. 55, no. 7. American Institute of Physics, 2014. ista: Jakšić V, Pillet C, Seiringer R. 2014. Introduction. Journal of Mathematical Physics. 55(7), 075101. mla: Jakšić, Vojkan, et al. “Introduction.” Journal of Mathematical Physics, vol. 55, no. 7, 075101, American Institute of Physics, 2014, doi:10.1063/1.4884877. short: V. Jakšić, C. Pillet, R. Seiringer, Journal of Mathematical Physics 55 (2014). date_created: 2018-12-11T11:54:12Z date_published: 2014-07-01T00:00:00Z date_updated: 2021-01-12T06:53:25Z day: '01' department: - _id: RoSe doi: 10.1063/1.4884877 intvolume: ' 55' issue: '7' language: - iso: eng month: '07' oa_version: None publication: Journal of Mathematical Physics publication_status: published publisher: American Institute of Physics publist_id: '5284' quality_controlled: '1' scopus_import: 1 status: public title: Introduction type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2014' ... --- _id: '1889' abstract: - lang: eng text: We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but also includes direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity. acknowledgement: We would like to thank Max Lein and Andreas Deuchert for valuable suggestions and remarks. Partial financial support by the NSERC (R.S.) is gratefully acknowledged. article_number: '1450012' article_processing_charge: No article_type: original author: - first_name: Gerhard full_name: Bräunlich, Gerhard last_name: Bräunlich - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Bräunlich G, Hainzl C, Seiringer R. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. 2014;26(7). doi:10.1142/S0129055X14500123 apa: Bräunlich, G., Hainzl, C., & Seiringer, R. (2014). Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X14500123 chicago: Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” Reviews in Mathematical Physics. World Scientific Publishing, 2014. https://doi.org/10.1142/S0129055X14500123. ieee: G. Bräunlich, C. Hainzl, and R. Seiringer, “Translation-invariant quasi-free states for fermionic systems and the BCS approximation,” Reviews in Mathematical Physics, vol. 26, no. 7. World Scientific Publishing, 2014. ista: Bräunlich G, Hainzl C, Seiringer R. 2014. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. 26(7), 1450012. mla: Bräunlich, Gerhard, et al. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” Reviews in Mathematical Physics, vol. 26, no. 7, 1450012, World Scientific Publishing, 2014, doi:10.1142/S0129055X14500123. short: G. Bräunlich, C. Hainzl, R. Seiringer, Reviews in Mathematical Physics 26 (2014). date_created: 2018-12-11T11:54:33Z date_published: 2014-08-01T00:00:00Z date_updated: 2022-06-07T09:03:09Z day: '01' department: - _id: RoSe doi: 10.1142/S0129055X14500123 external_id: arxiv: - '1305.5135' intvolume: ' 26' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1305.5135 month: '08' oa: 1 oa_version: Submitted Version publication: Reviews in Mathematical Physics publication_status: published publisher: World Scientific Publishing publist_id: '5206' quality_controlled: '1' scopus_import: '1' status: public title: Translation-invariant quasi-free states for fermionic systems and the BCS approximation type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2014' ... --- _id: '1904' abstract: - lang: eng text: We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation with a time-dependent potential and we show the existence of the wave operator in Schatten spaces. author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Mathieu full_name: Lewin, Mathieu last_name: Lewin - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Lewin M, Lieb É, Seiringer R. Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society. 2014;16(7):1507-1526. doi:10.4171/JEMS/467 apa: Frank, R., Lewin, M., Lieb, É., & Seiringer, R. (2014). Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/467 chicago: Frank, Rupert, Mathieu Lewin, Élliott Lieb, and Robert Seiringer. “Strichartz Inequality for Orthonormal Functions.” Journal of the European Mathematical Society. European Mathematical Society, 2014. https://doi.org/10.4171/JEMS/467. ieee: R. Frank, M. Lewin, É. Lieb, and R. Seiringer, “Strichartz inequality for orthonormal functions,” Journal of the European Mathematical Society, vol. 16, no. 7. European Mathematical Society, pp. 1507–1526, 2014. ista: Frank R, Lewin M, Lieb É, Seiringer R. 2014. Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society. 16(7), 1507–1526. mla: Frank, Rupert, et al. “Strichartz Inequality for Orthonormal Functions.” Journal of the European Mathematical Society, vol. 16, no. 7, European Mathematical Society, 2014, pp. 1507–26, doi:10.4171/JEMS/467. short: R. Frank, M. Lewin, É. Lieb, R. Seiringer, Journal of the European Mathematical Society 16 (2014) 1507–1526. date_created: 2018-12-11T11:54:38Z date_published: 2014-08-23T00:00:00Z date_updated: 2021-01-12T06:53:58Z day: '23' department: - _id: RoSe doi: 10.4171/JEMS/467 intvolume: ' 16' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1306.1309 month: '08' oa: 1 oa_version: Submitted Version page: 1507 - 1526 project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: Journal of the European Mathematical Society publication_status: published publisher: European Mathematical Society publist_id: '5191' quality_controlled: '1' scopus_import: 1 status: public title: Strichartz inequality for orthonormal functions type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2014' ... --- _id: '1918' abstract: - lang: eng text: As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc < N-K, where K is the maximal number of electrons that can be removed at Zc without changing the energy. article_number: '1350021' author: - first_name: Jacopo full_name: Bellazzini, Jacopo last_name: Bellazzini - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Bellazzini J, Frank R, Lieb É, Seiringer R. Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics. 2014;26(1). doi:10.1142/S0129055X13500219 apa: Bellazzini, J., Frank, R., Lieb, É., & Seiringer, R. (2014). Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X13500219 chicago: Bellazzini, Jacopo, Rupert Frank, Élliott Lieb, and Robert Seiringer. “Existence of Ground States for Negative Ions at the Binding Threshold.” Reviews in Mathematical Physics. World Scientific Publishing, 2014. https://doi.org/10.1142/S0129055X13500219. ieee: J. Bellazzini, R. Frank, É. Lieb, and R. Seiringer, “Existence of ground states for negative ions at the binding threshold,” Reviews in Mathematical Physics, vol. 26, no. 1. World Scientific Publishing, 2014. ista: Bellazzini J, Frank R, Lieb É, Seiringer R. 2014. Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics. 26(1), 1350021. mla: Bellazzini, Jacopo, et al. “Existence of Ground States for Negative Ions at the Binding Threshold.” Reviews in Mathematical Physics, vol. 26, no. 1, 1350021, World Scientific Publishing, 2014, doi:10.1142/S0129055X13500219. short: J. Bellazzini, R. Frank, É. Lieb, R. Seiringer, Reviews in Mathematical Physics 26 (2014). date_created: 2018-12-11T11:54:42Z date_published: 2014-02-01T00:00:00Z date_updated: 2021-01-12T06:54:04Z day: '01' department: - _id: RoSe doi: 10.1142/S0129055X13500219 intvolume: ' 26' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1301.5370 month: '02' oa: 1 oa_version: Submitted Version project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: Reviews in Mathematical Physics publication_status: published publisher: World Scientific Publishing publist_id: '5176' quality_controlled: '1' scopus_import: 1 status: public title: Existence of ground states for negative ions at the binding threshold type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2014' ... --- _id: '1935' abstract: - lang: eng text: 'We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.' acknowledgement: "2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\r\n\r\nThe research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G. and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part of a project started in collaboration with Joel Lebowitz, whom we thank for many useful discussions and for his constant encouragement." article_processing_charge: No article_type: original author: - first_name: Alessandro full_name: Giuliani, Alessandro last_name: Giuliani - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 2014;331:333-350. doi:10.1007/s00220-014-1923-2 apa: Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-1923-2 chicago: Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” Communications in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s00220-014-1923-2. ieee: A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” Communications in Mathematical Physics, vol. 331. Springer, pp. 333–350, 2014. ista: Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350. mla: Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” Communications in Mathematical Physics, vol. 331, Springer, 2014, pp. 333–50, doi:10.1007/s00220-014-1923-2. short: A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350. date_created: 2018-12-11T11:54:48Z date_published: 2014-10-01T00:00:00Z date_updated: 2022-05-24T08:32:50Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00220-014-1923-2 external_id: arxiv: - '1304.6344' file: - access_level: open_access checksum: c8423271cd1e1ba9e44c47af75efe7b6 content_type: application/pdf creator: dernst date_created: 2022-05-24T08:30:40Z date_updated: 2022-05-24T08:30:40Z file_id: '11409' file_name: 2014_CommMathPhysics_Giuliani.pdf file_size: 334064 relation: main_file success: 1 file_date_updated: 2022-05-24T08:30:40Z has_accepted_license: '1' intvolume: ' 331' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 333 - 350 publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer publist_id: '5159' quality_controlled: '1' scopus_import: '1' status: public title: Formation of stripes and slabs near the ferromagnetic transition type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 331 year: '2014' ... --- _id: '2029' abstract: - lang: eng text: Spin-wave theory is a key ingredient in our comprehension of quantum spin systems, and is used successfully for understanding a wide range of magnetic phenomena, including magnon condensation and stability of patterns in dipolar systems. Nevertheless, several decades of research failed to establish the validity of spin-wave theory rigorously, even for the simplest models of quantum spins. A rigorous justification of the method for the three-dimensional quantum Heisenberg ferromagnet at low temperatures is presented here. We derive sharp bounds on its free energy by combining a bosonic formulation of the model introduced by Holstein and Primakoff with probabilistic estimates and operator inequalities. acknowledgement: 239694; ERC; European Research Council article_number: '20003' author: - first_name: Michele full_name: Correggi, Michele last_name: Correggi - first_name: Alessandro full_name: Giuliani, Alessandro last_name: Giuliani - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Correggi M, Giuliani A, Seiringer R. Validity of spin-wave theory for the quantum Heisenberg model. EPL. 2014;108(2). doi:10.1209/0295-5075/108/20003 apa: Correggi, M., Giuliani, A., & Seiringer, R. (2014). Validity of spin-wave theory for the quantum Heisenberg model. EPL. IOP Publishing Ltd. https://doi.org/10.1209/0295-5075/108/20003 chicago: Correggi, Michele, Alessandro Giuliani, and Robert Seiringer. “Validity of Spin-Wave Theory for the Quantum Heisenberg Model.” EPL. IOP Publishing Ltd., 2014. https://doi.org/10.1209/0295-5075/108/20003. ieee: M. Correggi, A. Giuliani, and R. Seiringer, “Validity of spin-wave theory for the quantum Heisenberg model,” EPL, vol. 108, no. 2. IOP Publishing Ltd., 2014. ista: Correggi M, Giuliani A, Seiringer R. 2014. Validity of spin-wave theory for the quantum Heisenberg model. EPL. 108(2), 20003. mla: Correggi, Michele, et al. “Validity of Spin-Wave Theory for the Quantum Heisenberg Model.” EPL, vol. 108, no. 2, 20003, IOP Publishing Ltd., 2014, doi:10.1209/0295-5075/108/20003. short: M. Correggi, A. Giuliani, R. Seiringer, EPL 108 (2014). date_created: 2018-12-11T11:55:18Z date_published: 2014-10-13T00:00:00Z date_updated: 2021-01-12T06:54:50Z day: '13' department: - _id: RoSe doi: 10.1209/0295-5075/108/20003 intvolume: ' 108' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1404.4717 month: '10' oa: 1 oa_version: Submitted Version publication: EPL publication_status: published publisher: IOP Publishing Ltd. publist_id: '5044' quality_controlled: '1' scopus_import: 1 status: public title: Validity of spin-wave theory for the quantum Heisenberg model type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 108 year: '2014' ... --- _id: '2186' abstract: - lang: eng text: We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ℝ3. Moreover, we show that an exponential energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs. author: - first_name: Thomas full_name: Chen, Thomas last_name: Chen - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Nataša full_name: Pavlović, Nataša last_name: Pavlović - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Chen T, Hainzl C, Pavlović N, Seiringer R. On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. Letters in Mathematical Physics. 2014;104(7):871-891. doi:10.1007/s11005-014-0693-2 apa: Chen, T., Hainzl, C., Pavlović, N., & Seiringer, R. (2014). On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-014-0693-2 chicago: Chen, Thomas, Christian Hainzl, Nataša Pavlović, and Robert Seiringer. “On the Well-Posedness and Scattering for the Gross-Pitaevskii Hierarchy via Quantum de Finetti.” Letters in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s11005-014-0693-2. ieee: T. Chen, C. Hainzl, N. Pavlović, and R. Seiringer, “On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti,” Letters in Mathematical Physics, vol. 104, no. 7. Springer, pp. 871–891, 2014. ista: Chen T, Hainzl C, Pavlović N, Seiringer R. 2014. On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti. Letters in Mathematical Physics. 104(7), 871–891. mla: Chen, Thomas, et al. “On the Well-Posedness and Scattering for the Gross-Pitaevskii Hierarchy via Quantum de Finetti.” Letters in Mathematical Physics, vol. 104, no. 7, Springer, 2014, pp. 871–91, doi:10.1007/s11005-014-0693-2. short: T. Chen, C. Hainzl, N. Pavlović, R. Seiringer, Letters in Mathematical Physics 104 (2014) 871–891. date_created: 2018-12-11T11:56:12Z date_published: 2014-05-07T00:00:00Z date_updated: 2021-01-12T06:55:51Z day: '07' department: - _id: RoSe doi: 10.1007/s11005-014-0693-2 intvolume: ' 104' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1311.2136 month: '05' oa: 1 oa_version: Submitted Version page: 871 - 891 project: - _id: 26450934-B435-11E9-9278-68D0E5697425 name: NSERC Postdoctoral fellowship publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4793' quality_controlled: '1' scopus_import: 1 status: public title: On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 104 year: '2014' ... --- _id: '10814' abstract: - lang: eng text: We review recent progress towards a rigorous understanding of the excitation spectrum of bosonic quantum many-body systems. In particular, we explain how one can rigorously establish the predictions resulting from the Bogoliubov approximation in the mean field limit. The latter predicts that the spectrum is made up of elementary excitations, whose energy behaves linearly in the momentum for small momentum. This property is crucial for the superfluid behavior of the system. We also discuss a list of open problems in this field. article_processing_charge: No article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. The excitation spectrum for Bose fluids with weak interactions. Jahresbericht der Deutschen Mathematiker-Vereinigung. 2014;116:21-41. doi:10.1365/s13291-014-0083-9 apa: Seiringer, R. (2014). The excitation spectrum for Bose fluids with weak interactions. Jahresbericht Der Deutschen Mathematiker-Vereinigung. Springer Nature. https://doi.org/10.1365/s13291-014-0083-9 chicago: Seiringer, Robert. “The Excitation Spectrum for Bose Fluids with Weak Interactions.” Jahresbericht Der Deutschen Mathematiker-Vereinigung. Springer Nature, 2014. https://doi.org/10.1365/s13291-014-0083-9. ieee: R. Seiringer, “The excitation spectrum for Bose fluids with weak interactions,” Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 116. Springer Nature, pp. 21–41, 2014. ista: Seiringer R. 2014. The excitation spectrum for Bose fluids with weak interactions. Jahresbericht der Deutschen Mathematiker-Vereinigung. 116, 21–41. mla: Seiringer, Robert. “The Excitation Spectrum for Bose Fluids with Weak Interactions.” Jahresbericht Der Deutschen Mathematiker-Vereinigung, vol. 116, Springer Nature, 2014, pp. 21–41, doi:10.1365/s13291-014-0083-9. short: R. Seiringer, Jahresbericht Der Deutschen Mathematiker-Vereinigung 116 (2014) 21–41. date_created: 2022-03-04T07:54:39Z date_published: 2014-03-01T00:00:00Z date_updated: 2023-09-05T14:19:47Z day: '01' department: - _id: RoSe doi: 10.1365/s13291-014-0083-9 intvolume: ' 116' keyword: - General Medicine language: - iso: eng month: '03' oa_version: None page: 21-41 publication: Jahresbericht der Deutschen Mathematiker-Vereinigung publication_identifier: eissn: - 1869-7135 issn: - 0012-0456 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The excitation spectrum for Bose fluids with weak interactions type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 116 year: '2014' ... --- _id: '8044' abstract: - lang: eng text: Many questions concerning models in quantum mechanics require a detailed analysis of the spectrum of the corresponding Hamiltonian, a linear operator on a suitable Hilbert space. Of particular relevance for an understanding of the low-temperature properties of a system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such system are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system. article_processing_charge: No author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Seiringer R. Structure of the excitation spectrum for many-body quantum systems. In: Proceeding of the International Congress of Mathematicans. Vol 3. International Congress of Mathematicians; 2014:1175-1194.' apa: 'Seiringer, R. (2014). Structure of the excitation spectrum for many-body quantum systems. In Proceeding of the International Congress of Mathematicans (Vol. 3, pp. 1175–1194). Seoul, South Korea: International Congress of Mathematicians.' chicago: Seiringer, Robert. “Structure of the Excitation Spectrum for Many-Body Quantum Systems.” In Proceeding of the International Congress of Mathematicans, 3:1175–94. International Congress of Mathematicians, 2014. ieee: R. Seiringer, “Structure of the excitation spectrum for many-body quantum systems,” in Proceeding of the International Congress of Mathematicans, Seoul, South Korea, 2014, vol. 3, pp. 1175–1194. ista: 'Seiringer R. 2014. Structure of the excitation spectrum for many-body quantum systems. Proceeding of the International Congress of Mathematicans. ICM: International Congress of Mathematicans vol. 3, 1175–1194.' mla: Seiringer, Robert. “Structure of the Excitation Spectrum for Many-Body Quantum Systems.” Proceeding of the International Congress of Mathematicans, vol. 3, International Congress of Mathematicians, 2014, pp. 1175–94. short: R. Seiringer, in:, Proceeding of the International Congress of Mathematicans, International Congress of Mathematicians, 2014, pp. 1175–1194. conference: end_date: 2014-08-21 location: Seoul, South Korea name: 'ICM: International Congress of Mathematicans' start_date: 2014-08-13 date_created: 2020-06-29T07:59:35Z date_published: 2014-08-01T00:00:00Z date_updated: 2023-10-17T11:12:33Z day: '01' department: - _id: RoSe intvolume: ' 3' language: - iso: eng main_file_link: - open_access: '1' url: http://www.icm2014.org/en/vod/proceedings.html month: '08' oa: 1 oa_version: Published Version page: 1175-1194 publication: Proceeding of the International Congress of Mathematicans publication_identifier: isbn: - '9788961058063' publication_status: published publisher: International Congress of Mathematicians quality_controlled: '1' scopus_import: '1' status: public title: Structure of the excitation spectrum for many-body quantum systems type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2014' ... --- _id: '2281' abstract: - lang: eng text: We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength a satisfies {Mathematical expression}, where Q is the unique positive radial solution of {Mathematical expression} in {Mathematical expression}. We present a detailed analysis of the behavior of minimizers as a approaches a*, where all the mass concentrates at a global minimum of the trapping potential. article_processing_charge: No article_type: original author: - first_name: Yujin full_name: Guo, Yujin last_name: Guo - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Guo Y, Seiringer R. On the mass concentration for Bose-Einstein condensates with attractive interactions. Letters in Mathematical Physics. 2014;104(2):141-156. doi:10.1007/s11005-013-0667-9 apa: Guo, Y., & Seiringer, R. (2014). On the mass concentration for Bose-Einstein condensates with attractive interactions. Letters in Mathematical Physics. Springer. https://doi.org/10.1007/s11005-013-0667-9 chicago: Guo, Yujin, and Robert Seiringer. “On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions.” Letters in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s11005-013-0667-9. ieee: Y. Guo and R. Seiringer, “On the mass concentration for Bose-Einstein condensates with attractive interactions,” Letters in Mathematical Physics, vol. 104, no. 2. Springer, pp. 141–156, 2014. ista: Guo Y, Seiringer R. 2014. On the mass concentration for Bose-Einstein condensates with attractive interactions. Letters in Mathematical Physics. 104(2), 141–156. mla: Guo, Yujin, and Robert Seiringer. “On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions.” Letters in Mathematical Physics, vol. 104, no. 2, Springer, 2014, pp. 141–56, doi:10.1007/s11005-013-0667-9. short: Y. Guo, R. Seiringer, Letters in Mathematical Physics 104 (2014) 141–156. date_created: 2018-12-11T11:56:44Z date_published: 2014-02-01T00:00:00Z date_updated: 2024-02-14T12:19:42Z day: '01' department: - _id: RoSe doi: 10.1007/s11005-013-0667-9 external_id: arxiv: - '1301.5682' intvolume: ' 104' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1301.5682 month: '02' oa: 1 oa_version: Preprint page: 141 - 156 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4653' quality_controlled: '1' scopus_import: '1' status: public title: On the mass concentration for Bose-Einstein condensates with attractive interactions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 104 year: '2014' ... --- _id: '2297' abstract: - lang: eng text: We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The presentation includes a discussion of Bose-Einstein condensation, the excitation spectrum for trapped gases and its relation to superfluidity, as well as the appearance of quantized vortices in rotating systems. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation. author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Seiringer R. Hot topics in cold gases: A mathematical physics perspective. Japanese Journal of Mathematics. 2013;8(2):185-232. doi:10.1007/s11537-013-1264-5' apa: 'Seiringer, R. (2013). Hot topics in cold gases: A mathematical physics perspective. Japanese Journal of Mathematics. Springer. https://doi.org/10.1007/s11537-013-1264-5' chicago: 'Seiringer, Robert. “Hot Topics in Cold Gases: A Mathematical Physics Perspective.” Japanese Journal of Mathematics. Springer, 2013. https://doi.org/10.1007/s11537-013-1264-5.' ieee: 'R. Seiringer, “Hot topics in cold gases: A mathematical physics perspective,” Japanese Journal of Mathematics, vol. 8, no. 2. Springer, pp. 185–232, 2013.' ista: 'Seiringer R. 2013. Hot topics in cold gases: A mathematical physics perspective. Japanese Journal of Mathematics. 8(2), 185–232.' mla: 'Seiringer, Robert. “Hot Topics in Cold Gases: A Mathematical Physics Perspective.” Japanese Journal of Mathematics, vol. 8, no. 2, Springer, 2013, pp. 185–232, doi:10.1007/s11537-013-1264-5.' short: R. Seiringer, Japanese Journal of Mathematics 8 (2013) 185–232. date_created: 2018-12-11T11:56:50Z date_published: 2013-09-24T00:00:00Z date_updated: 2021-01-12T06:56:36Z day: '24' department: - _id: RoSe doi: 10.1007/s11537-013-1264-5 external_id: arxiv: - '0908.3686' intvolume: ' 8' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/0908.3686 month: '09' oa: 1 oa_version: Preprint page: 185 - 232 publication: Japanese Journal of Mathematics publication_status: published publisher: Springer publist_id: '4631' quality_controlled: '1' scopus_import: 1 status: public title: 'Hot topics in cold gases: A mathematical physics perspective' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 8 year: '2013' ... --- _id: '2300' abstract: - lang: eng text: We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long-range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a critical value Jc, then the ground state is homogeneous and ferromagnetic. As the critical value is approached from smaller values of J, it is believed that the ground state consists of a periodic array of stripes (d=2) or slabs (d=3), all of the same size and alternating magnetization. Here we prove rigorously that the ground state energy per site converges to that of the optimal periodic striped or slabbed state, in the limit that J tends to the ferromagnetic transition point. While this theorem does not prove rigorously that the ground state is precisely striped or slabbed, it does prove that in any suitably large box the ground state is striped or slabbed with high probability. article_number: '064401' author: - first_name: Alessandro full_name: Giuliani, Alessandro last_name: Giuliani - first_name: Élliott full_name: Lieb, Élliott last_name: Lieb - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Giuliani A, Lieb É, Seiringer R. Realization of stripes and slabs in two and three dimensions. Physical Review B. 2013;88(6). doi:10.1103/PhysRevB.88.064401 apa: Giuliani, A., Lieb, É., & Seiringer, R. (2013). Realization of stripes and slabs in two and three dimensions. Physical Review B. American Physical Society. https://doi.org/10.1103/PhysRevB.88.064401 chicago: Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Realization of Stripes and Slabs in Two and Three Dimensions.” Physical Review B. American Physical Society, 2013. https://doi.org/10.1103/PhysRevB.88.064401. ieee: A. Giuliani, É. Lieb, and R. Seiringer, “Realization of stripes and slabs in two and three dimensions,” Physical Review B, vol. 88, no. 6. American Physical Society, 2013. ista: Giuliani A, Lieb É, Seiringer R. 2013. Realization of stripes and slabs in two and three dimensions. Physical Review B. 88(6), 064401. mla: Giuliani, Alessandro, et al. “Realization of Stripes and Slabs in Two and Three Dimensions.” Physical Review B, vol. 88, no. 6, 064401, American Physical Society, 2013, doi:10.1103/PhysRevB.88.064401. short: A. Giuliani, É. Lieb, R. Seiringer, Physical Review B 88 (2013). date_created: 2018-12-11T11:56:51Z date_published: 2013-08-01T00:00:00Z date_updated: 2021-01-12T06:56:38Z day: '01' department: - _id: RoSe doi: 10.1103/PhysRevB.88.064401 external_id: arxiv: - '1305.5323' intvolume: ' 88' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1305.5323 month: '08' oa: 1 oa_version: Preprint publication: Physical Review B publication_status: published publisher: American Physical Society publist_id: '4627' quality_controlled: '1' scopus_import: 1 status: public title: Realization of stripes and slabs in two and three dimensions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 88 year: '2013' ... --- _id: '2318' abstract: - lang: eng text: 'We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential. ' acknowledgement: 'Partial financial support by NSERC ' author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. Absence of bound states implies non-negativity of the scattering length. Journal of Spectral Theory. 2012;2(3):321-328. doi:10.4171/JST/31 apa: Seiringer, R. (2012). Absence of bound states implies non-negativity of the scattering length. Journal of Spectral Theory. European Mathematical Society. https://doi.org/10.4171/JST/31 chicago: Seiringer, Robert. “Absence of Bound States Implies Non-Negativity of the Scattering Length.” Journal of Spectral Theory. European Mathematical Society, 2012. https://doi.org/10.4171/JST/31. ieee: R. Seiringer, “Absence of bound states implies non-negativity of the scattering length,” Journal of Spectral Theory, vol. 2, no. 3. European Mathematical Society, pp. 321–328, 2012. ista: Seiringer R. 2012. Absence of bound states implies non-negativity of the scattering length. Journal of Spectral Theory. 2(3), 321–328. mla: Seiringer, Robert. “Absence of Bound States Implies Non-Negativity of the Scattering Length.” Journal of Spectral Theory, vol. 2, no. 3, European Mathematical Society, 2012, pp. 321–28, doi:10.4171/JST/31. short: R. Seiringer, Journal of Spectral Theory 2 (2012) 321–328. date_created: 2018-12-11T11:56:58Z date_published: 2012-06-24T00:00:00Z date_updated: 2021-01-12T06:56:44Z day: '24' department: - _id: RoSe doi: 10.4171/JST/31 intvolume: ' 2' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1204.0435 month: '06' oa: 1 oa_version: Preprint page: 321-328 publication: Journal of Spectral Theory publication_status: published publisher: European Mathematical Society publist_id: '4609' quality_controlled: '1' status: public title: Absence of bound states implies non-negativity of the scattering length type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2012' ...