--- _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' ...