--- _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' ...