--- _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 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' ...