--- _id: '14931' abstract: - lang: eng text: We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15]. acknowledgement: A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged. article_number: '110320' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110320' apa: 'Lauritsen, A. B., & Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110320' chicago: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110320.' ieee: 'A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” Journal of Functional Analysis, vol. 286, no. 7. Elsevier, 2024.' ista: 'Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.' mla: 'Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” Journal of Functional Analysis, vol. 286, no. 7, 110320, Elsevier, 2024, doi:10.1016/j.jfa.2024.110320.' short: A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024). date_created: 2024-02-04T23:00:53Z date_published: 2024-01-24T00:00:00Z date_updated: 2024-03-28T10:54:02Z day: '24' department: - _id: RoSe doi: 10.1016/j.jfa.2024.110320 ec_funded: 1 external_id: arxiv: - '2301.04894' intvolume: ' 286' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1016/j.jfa.2024.110320 month: '01' 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: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Journal of Functional Analysis publication_identifier: eissn: - 1096--0783 issn: - 0022-1236 publication_status: epub_ahead publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: 'Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 286 year: '2024' ... --- _id: '12183' abstract: - lang: eng text: We consider a gas of n bosonic particles confined in a box [−ℓ/2,ℓ/2]3 with Neumann boundary conditions. We prove Bose–Einstein condensation in the Gross–Pitaevskii regime, with an optimal bound on the condensate depletion. Moreover, our lower bound for the ground state energy in a small box [−ℓ/2,ℓ/2]3 implies (via Neumann bracketing) a lower bound for the ground state energy of N bosons in a large box [−L/2,L/2]3 with density ρ=N/L3 in the thermodynamic limit. acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. 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: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Boccato C, Seiringer R. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 2023;24:1505-1560. doi:10.1007/s00023-022-01252-3 apa: Boccato, C., & Seiringer, R. (2023). The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01252-3 chicago: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” Annales Henri Poincare. Springer Nature, 2023. https://doi.org/10.1007/s00023-022-01252-3. ieee: C. Boccato and R. Seiringer, “The Bose Gas in a box with Neumann boundary conditions,” Annales Henri Poincare, vol. 24. Springer Nature, pp. 1505–1560, 2023. ista: Boccato C, Seiringer R. 2023. The Bose Gas in a box with Neumann boundary conditions. Annales Henri Poincare. 24, 1505–1560. mla: Boccato, Chiara, and Robert Seiringer. “The Bose Gas in a Box with Neumann Boundary Conditions.” Annales Henri Poincare, vol. 24, Springer Nature, 2023, pp. 1505–60, doi:10.1007/s00023-022-01252-3. short: C. Boccato, R. Seiringer, Annales Henri Poincare 24 (2023) 1505–1560. date_created: 2023-01-15T23:00:52Z date_published: 2023-05-01T00:00:00Z date_updated: 2023-08-16T11:34:03Z day: '01' department: - _id: RoSe doi: 10.1007/s00023-022-01252-3 ec_funded: 1 external_id: arxiv: - '2205.15284' isi: - '000910751800002' intvolume: ' 24' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2205.15284 month: '05' oa: 1 oa_version: Preprint page: 1505-1560 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The Bose Gas in a box with Neumann boundary conditions type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '12430' abstract: - lang: eng text: We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively. article_number: '2350006' article_processing_charge: No article_type: original author: - first_name: Marco full_name: Falconi, Marco last_name: Falconi - 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: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - 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: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 2023;35(4). doi:10.1142/S0129055X2350006X apa: Falconi, M., Leopold, N. K., Mitrouskas, D. J., & Petrat, S. P. (2023). Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X2350006X chicago: Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/S0129055X2350006X. ieee: M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov dynamics and higher-order corrections for the regularized Nelson model,” Reviews in Mathematical Physics, vol. 35, no. 4. World Scientific Publishing, 2023. ista: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics and higher-order corrections for the regularized Nelson model. Reviews in Mathematical Physics. 35(4), 2350006. mla: Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized Nelson Model.” Reviews in Mathematical Physics, vol. 35, no. 4, 2350006, World Scientific Publishing, 2023, doi:10.1142/S0129055X2350006X. short: M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical Physics 35 (2023). date_created: 2023-01-29T23:00:59Z date_published: 2023-01-09T00:00:00Z date_updated: 2023-08-16T11:47:27Z day: '09' department: - _id: RoSe doi: 10.1142/S0129055X2350006X external_id: arxiv: - '2110.00458' isi: - '000909760300001' intvolume: ' 35' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: ' https://doi.org/10.48550/arXiv.2110.00458' month: '01' oa: 1 oa_version: Preprint publication: Reviews in Mathematical Physics publication_identifier: issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Bogoliubov dynamics and higher-order corrections for the regularized Nelson model type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 35 year: '2023' ... --- _id: '14374' abstract: - lang: eng text: "Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality.\r\n\r\nIn the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Roos B. Boundary superconductivity in BCS theory. 2023. doi:10.15479/at:ista:14374 apa: Roos, B. (2023). Boundary superconductivity in BCS theory. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14374 chicago: Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14374. ieee: B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023. ista: Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science and Technology Austria. mla: Roos, Barbara. Boundary Superconductivity in BCS Theory. Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14374. short: B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023. date_created: 2023-09-28T14:23:04Z date_published: 2023-09-30T00:00:00Z date_updated: 2023-10-27T10:37:30Z day: '30' ddc: - '515' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:14374 ec_funded: 1 file: - access_level: open_access checksum: ef039ffc3de2cb8dee5b14110938e9b6 content_type: application/pdf creator: broos date_created: 2023-10-06T11:35:56Z date_updated: 2023-10-06T11:35:56Z file_id: '14398' file_name: phd-thesis-draft_pdfa_acrobat.pdf file_size: 2365702 relation: main_file - access_level: closed checksum: 81dcac33daeefaf0111db52f41bb1fd0 content_type: application/x-zip-compressed creator: broos date_created: 2023-10-06T11:38:01Z date_updated: 2023-10-06T11:38:01Z file_id: '14399' file_name: Version5.zip file_size: 4691734 relation: source_file file_date_updated: 2023-10-06T11:38:01Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '09' oa: 1 oa_version: Published Version page: '206' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication_identifier: issn: - 2663 - 337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '13207' relation: part_of_dissertation status: public - id: '10850' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Boundary superconductivity in BCS theory tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2023' ... --- _id: '13207' abstract: - lang: eng text: We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg–Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity. acknowledgement: We thank Egor Babaev for encouraging us to study this problem, and Rupert Frank for many fruitful discussions. scussions. Funding. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 (Barbara Roos and Robert Seiringer) is gratefully acknowledged. article_processing_charge: No article_type: original author: - first_name: Christian full_name: Hainzl, Christian last_name: Hainzl - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Hainzl C, Roos B, Seiringer R. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 2023;12(4):1507–1540. doi:10.4171/JST/439 apa: Hainzl, C., Roos, B., & Seiringer, R. (2023). Boundary superconductivity in the BCS model. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/439 chicago: Hainzl, Christian, Barbara Roos, and Robert Seiringer. “Boundary Superconductivity in the BCS Model.” Journal of Spectral Theory. EMS Press, 2023. https://doi.org/10.4171/JST/439. ieee: C. Hainzl, B. Roos, and R. Seiringer, “Boundary superconductivity in the BCS model,” Journal of Spectral Theory, vol. 12, no. 4. EMS Press, pp. 1507–1540, 2023. ista: Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 12(4), 1507–1540. mla: Hainzl, Christian, et al. “Boundary Superconductivity in the BCS Model.” Journal of Spectral Theory, vol. 12, no. 4, EMS Press, 2023, pp. 1507–1540, doi:10.4171/JST/439. short: C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540. date_created: 2023-07-10T16:35:45Z date_published: 2023-05-18T00:00:00Z date_updated: 2023-10-27T10:37:29Z day: '18' ddc: - '530' department: - _id: GradSch - _id: RoSe doi: 10.4171/JST/439 ec_funded: 1 external_id: arxiv: - '2201.08090' isi: - '000997933500008' file: - access_level: open_access checksum: 5501da33be010b5c81440438287584d5 content_type: application/pdf creator: alisjak date_created: 2023-07-11T08:19:15Z date_updated: 2023-07-11T08:19:15Z file_id: '13208' file_name: 2023_EMS_Hainzl.pdf file_size: 304619 relation: main_file success: 1 file_date_updated: 2023-07-11T08:19:15Z has_accepted_license: '1' intvolume: ' 12' isi: 1 issue: '4' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '05' oa: 1 oa_version: Published Version page: 1507–1540 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Journal of Spectral Theory publication_identifier: eissn: - 1664-0403 issn: - 1664-039X publication_status: published publisher: EMS Press quality_controlled: '1' related_material: record: - id: '14374' relation: dissertation_contains status: public status: public title: Boundary superconductivity in the BCS model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 12 year: '2023' ... --- _id: '14441' abstract: - lang: eng text: We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation. acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3' apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3' chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.' ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” Communications in Mathematical Physics, vol. 404. Springer Nature, pp. 287–337, 2023.' ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.' mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.' short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337. date_created: 2023-10-22T22:01:13Z date_published: 2023-11-01T00:00:00Z date_updated: 2023-10-31T12:22:51Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00220-023-04841-3 ec_funded: 1 external_id: arxiv: - '2207.03156' file: - access_level: open_access checksum: 1ae49b39247cb6b40ff75997381581b8 content_type: application/pdf creator: dernst date_created: 2023-10-31T12:21:39Z date_updated: 2023-10-31T12:21:39Z file_id: '14477' file_name: 2023_CommMathPhysics_Brooks.pdf file_size: 832375 relation: main_file success: 1 file_date_updated: 2023-10-31T12:21:39Z has_accepted_license: '1' intvolume: ' 404' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 287-337 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 Nature quality_controlled: '1' scopus_import: '1' status: public title: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 404 year: '2023' ... --- _id: '13178' abstract: - lang: eng text: We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar. acknowledgement: This research was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.). article_processing_charge: Yes article_type: original author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mitrouskas DJ, Mysliwy K, Seiringer R. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 2023;11:1-52. doi:10.1017/fms.2023.45 apa: Mitrouskas, D. J., Mysliwy, K., & Seiringer, R. (2023). Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. Cambridge University Press. https://doi.org/10.1017/fms.2023.45 chicago: Mitrouskas, David Johannes, Krzysztof Mysliwy, and Robert Seiringer. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” Forum of Mathematics. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.45. ieee: D. J. Mitrouskas, K. Mysliwy, and R. Seiringer, “Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron,” Forum of Mathematics, vol. 11. Cambridge University Press, pp. 1–52, 2023. ista: Mitrouskas DJ, Mysliwy K, Seiringer R. 2023. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics. 11, 1–52. mla: Mitrouskas, David Johannes, et al. “Optimal Parabolic Upper Bound for the Energy-Momentum Relation of a Strongly Coupled Polaron.” Forum of Mathematics, vol. 11, Cambridge University Press, 2023, pp. 1–52, doi:10.1017/fms.2023.45. short: D.J. Mitrouskas, K. Mysliwy, R. Seiringer, Forum of Mathematics 11 (2023) 1–52. date_created: 2023-07-02T22:00:43Z date_published: 2023-06-13T00:00:00Z date_updated: 2023-11-02T12:30:50Z day: '13' ddc: - '500' department: - _id: RoSe doi: 10.1017/fms.2023.45 ec_funded: 1 external_id: arxiv: - '2203.02454' isi: - '001005008800001' file: - access_level: open_access checksum: f672eb7dd015c472c9a04f1b9bf9df7d content_type: application/pdf creator: alisjak date_created: 2023-07-03T10:36:25Z date_updated: 2023-07-03T10:36:25Z file_id: '13186' file_name: 2023_ForumofMathematics.Sigma_Mitrouskas.pdf file_size: 943192 relation: main_file success: 1 file_date_updated: 2023-07-03T10:36:25Z has_accepted_license: '1' intvolume: ' 11' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Published Version page: 1-52 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Forum of Mathematics publication_identifier: eissn: - 2050-5094 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 11 year: '2023' ... --- _id: '12869' abstract: - lang: eng text: 'We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately round cultures get a competitive advantage. We first analyse the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e. freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity and the central European plain has less clear cultural borders. ' acknowledgement: 'FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. ' article_processing_charge: No author: - first_name: Frederik Ravn full_name: Klausen, Frederik Ravn last_name: Klausen - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: 'Klausen FR, Lauritsen AB. Research data for: A stochastic cellular automaton model of culture formation. 2023. doi:10.15479/AT:ISTA:12869' apa: 'Klausen, F. R., & Lauritsen, A. B. (2023). Research data for: A stochastic cellular automaton model of culture formation. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:12869' chicago: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Research Data for: A Stochastic Cellular Automaton Model of Culture Formation.” Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/AT:ISTA:12869.' ieee: 'F. R. Klausen and A. B. Lauritsen, “Research data for: A stochastic cellular automaton model of culture formation.” Institute of Science and Technology Austria, 2023.' ista: 'Klausen FR, Lauritsen AB. 2023. Research data for: A stochastic cellular automaton model of culture formation, Institute of Science and Technology Austria, 10.15479/AT:ISTA:12869.' mla: 'Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. Research Data for: A Stochastic Cellular Automaton Model of Culture Formation. Institute of Science and Technology Austria, 2023, doi:10.15479/AT:ISTA:12869.' short: F.R. Klausen, A.B. Lauritsen, (2023). date_created: 2023-04-26T12:34:49Z date_published: 2023-04-26T00:00:00Z date_updated: 2023-11-13T07:47:29Z day: '26' ddc: - '000' department: - _id: GradSch - _id: RoSe doi: 10.15479/AT:ISTA:12869 file: - access_level: open_access checksum: 85ede12d38bb8d944022a8cba4d719f5 content_type: application/octet-stream creator: alaurits date_created: 2023-04-26T12:30:06Z date_updated: 2023-04-26T12:30:06Z file_id: '12870' file_name: README.md file_size: 4567 relation: main_file success: 1 - access_level: open_access checksum: 25bf79452ae895f9c8a20571a096b4c3 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:27:34Z date_updated: 2023-04-26T12:27:34Z file_id: '12871' file_name: simulations_era=10_flux_varied_europe.zip file_size: 732586731 relation: main_file success: 1 - access_level: open_access checksum: bca48d80ece73eb169aee7211a4a751a content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:29:53Z date_updated: 2023-04-26T12:29:53Z file_id: '12872' file_name: simulations_era=10_flux_varied_torus.zip file_size: 1743893150 relation: main_file success: 1 - access_level: open_access checksum: e77a655db15486a387a36362fbf0b665 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:29:19Z date_updated: 2023-04-26T12:29:19Z file_id: '12873' file_name: simulations_era=10_R_varied_torus.zip file_size: 878391851 relation: main_file success: 1 - access_level: open_access checksum: 8556406513adc4aa2e0417f46680f627 content_type: application/x-zip-compressed creator: alaurits date_created: 2023-04-26T12:30:05Z date_updated: 2023-04-26T12:30:05Z file_id: '12874' file_name: simulations_era=100.zip file_size: 201652478 relation: main_file success: 1 file_date_updated: 2023-04-26T12:30:06Z has_accepted_license: '1' license: https://creativecommons.org/publicdomain/zero/1.0/ month: '04' oa: 1 oa_version: Published Version publisher: Institute of Science and Technology Austria related_material: record: - id: '14505' relation: used_in_publication status: for_moderation - id: '12890' relation: used_in_publication status: public status: public title: 'Research data for: A stochastic cellular automaton model of culture formation' tmp: image: /images/cc_0.png legal_code_url: https://creativecommons.org/publicdomain/zero/1.0/legalcode name: Creative Commons Public Domain Dedication (CC0 1.0) short: CC0 (1.0) type: research_data user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12890' abstract: - lang: eng text: We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders. acknowledgement: Thanks to Kim Sneppen, Svend Krøjer, Peter Wildemann, Peter Rasmussen and Kent Bækgaard Lauritsen for discussions and suggestions. FRK acknowledges support from the Villum Foundation for support through the QMATH center of Excellence (Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs. article_number: '054307' article_processing_charge: No article_type: original author: - first_name: Frederik Ravn full_name: Klausen, Frederik Ravn last_name: Klausen - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Klausen FR, Lauritsen AB. Stochastic cellular automaton model of culture formation. Physical Review E. 2023;108(5). doi:10.1103/PhysRevE.108.054307 apa: Klausen, F. R., & Lauritsen, A. B. (2023). Stochastic cellular automaton model of culture formation. Physical Review E. American Physical Society. https://doi.org/10.1103/PhysRevE.108.054307 chicago: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” Physical Review E. American Physical Society, 2023. https://doi.org/10.1103/PhysRevE.108.054307. ieee: F. R. Klausen and A. B. Lauritsen, “Stochastic cellular automaton model of culture formation,” Physical Review E, vol. 108, no. 5. American Physical Society, 2023. ista: Klausen FR, Lauritsen AB. 2023. Stochastic cellular automaton model of culture formation. Physical Review E. 108(5), 054307. mla: Klausen, Frederik Ravn, and Asbjørn Bækgaard Lauritsen. “Stochastic Cellular Automaton Model of Culture Formation.” Physical Review E, vol. 108, no. 5, 054307, American Physical Society, 2023, doi:10.1103/PhysRevE.108.054307. short: F.R. Klausen, A.B. Lauritsen, Physical Review E 108 (2023). date_created: 2023-05-04T08:35:01Z date_published: 2023-11-08T00:00:00Z date_updated: 2023-11-13T07:47:30Z day: '08' department: - _id: GradSch - _id: RoSe doi: 10.1103/PhysRevE.108.054307 external_id: arxiv: - '2305.02153' intvolume: ' 108' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2305.02153 month: '11' oa: 1 oa_version: Preprint publication: Physical Review E publication_identifier: eissn: - 2470-0053 issn: - 2470-0045 publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: link: - relation: software url: https://github.com/FrederikRavnKlausen/model-for-culture-formation record: - id: '12869' relation: research_data status: public scopus_import: '1' status: public title: Stochastic cellular automaton model of culture formation type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 108 year: '2023' ... --- _id: '12911' abstract: - lang: eng text: 'This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.' acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813." article_number: '109963' article_processing_charge: No article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Augusto full_name: Gerolin, Augusto last_name: Gerolin - first_name: Lorenzo full_name: Portinale, Lorenzo id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87 last_name: Portinale citation: ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963 apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023. ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963. mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” Journal of Functional Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963. short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023). date_created: 2023-05-07T22:01:02Z date_published: 2023-08-15T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '15' department: - _id: RoSe - _id: JaMa doi: 10.1016/j.jfa.2023.109963 ec_funded: 1 external_id: arxiv: - '2106.11217' isi: - '000990804300001' intvolume: ' 285' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '08' oa: 1 oa_version: Preprint project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '9792' relation: earlier_version status: public scopus_import: '1' status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '14542' abstract: - lang: eng text: "It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit." acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427. article_number: '2360005 ' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 citation: ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2023. doi:10.1142/s0129055x2360005x apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/s0129055x2360005x. ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing, 2023. ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005. mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, 2360005, World Scientific Publishing, 2023, doi:10.1142/s0129055x2360005x. short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023). date_created: 2023-11-15T23:48:14Z date_published: 2023-10-31T00:00:00Z date_updated: 2023-11-20T10:04:38Z day: '31' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1142/s0129055x2360005x ec_funded: 1 external_id: arxiv: - '2301.05621' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1142/S0129055X2360005X month: '10' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta - _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b grant_number: I06427 name: Mathematical Challenges in BCS Theory of Superconductivity publication: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: epub_ahead publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Universality in low-dimensional BCS theory tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '14662' abstract: - lang: eng text: "We consider a class of polaron models, including the Fröhlich model, at zero total\r\nmomentum, and show that at sufficiently weak coupling there are no excited eigenvalues below\r\nthe essential spectrum." article_processing_charge: Yes article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. 2023;13(3):1045-1055. doi:10.4171/JST/469 apa: Seiringer, R. (2023). Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/469 chicago: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” Journal of Spectral Theory. EMS Press, 2023. https://doi.org/10.4171/JST/469. ieee: R. Seiringer, “Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling,” Journal of Spectral Theory, vol. 13, no. 3. EMS Press, pp. 1045–1055, 2023. ista: Seiringer R. 2023. Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling. Journal of Spectral Theory. 13(3), 1045–1055. mla: Seiringer, Robert. “Absence of Excited Eigenvalues for Fröhlich Type Polaron Models at Weak Coupling.” Journal of Spectral Theory, vol. 13, no. 3, EMS Press, 2023, pp. 1045–55, doi:10.4171/JST/469. short: R. Seiringer, Journal of Spectral Theory 13 (2023) 1045–1055. date_created: 2023-12-10T23:00:59Z date_published: 2023-11-25T00:00:00Z date_updated: 2023-12-11T12:12:14Z day: '25' ddc: - '510' department: - _id: RoSe doi: 10.4171/JST/469 external_id: arxiv: - '2210.17123' file: - access_level: open_access checksum: 9ce96ca87d56ea9a70d2eb9a32839f8d content_type: application/pdf creator: dernst date_created: 2023-12-11T12:03:12Z date_updated: 2023-12-11T12:03:12Z file_id: '14677' file_name: 2023_JST_Seiringer.pdf file_size: 201513 relation: main_file success: 1 file_date_updated: 2023-12-11T12:03:12Z has_accepted_license: '1' intvolume: ' 13' issue: '3' language: - iso: eng month: '11' oa: 1 oa_version: None page: 1045-1055 publication: Journal of Spectral Theory publication_identifier: eissn: - 1664-0403 issn: - 1664-039X publication_status: published publisher: EMS Press quality_controlled: '1' scopus_import: '1' status: public title: Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 13 year: '2023' ... --- _id: '13225' abstract: - lang: eng text: Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only |⋅|V^∈ℓ1(Z3). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy. acknowledgement: "RS was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). MP acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, Grant Agreement No. 802901). BS acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC AdG CLaQS (Grant Agreement No. 834782). NB and MP were supported by Gruppo Nazionale per la Fisica Matematica (GNFM) of Italy. NB was supported by the European Research Council’s Starting Grant FERMIMATH (Grant Agreement No. 101040991).\r\nOpen access funding provided by Università degli Studi di Milano within the CRUI-CARE Agreement." article_number: '65' article_processing_charge: Yes (via OA deal) article_type: original 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: Marcello full_name: Porta, Marcello last_name: Porta - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Benedikter NP, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 2023;247(4). doi:10.1007/s00205-023-01893-6 apa: Benedikter, N. P., Porta, M., Schlein, B., & Seiringer, R. (2023). Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01893-6 chicago: Benedikter, Niels P, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” Archive for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01893-6. ieee: N. P. Benedikter, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas with large interaction potential,” Archive for Rational Mechanics and Analysis, vol. 247, no. 4. Springer Nature, 2023. ista: Benedikter NP, Porta M, Schlein B, Seiringer R. 2023. Correlation energy of a weakly interacting Fermi gas with large interaction potential. Archive for Rational Mechanics and Analysis. 247(4), 65. mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential.” Archive for Rational Mechanics and Analysis, vol. 247, no. 4, 65, Springer Nature, 2023, doi:10.1007/s00205-023-01893-6. short: N.P. Benedikter, M. Porta, B. Schlein, R. Seiringer, Archive for Rational Mechanics and Analysis 247 (2023). date_created: 2023-07-16T22:01:08Z date_published: 2023-08-01T00:00:00Z date_updated: 2023-12-13T11:31:14Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00205-023-01893-6 ec_funded: 1 external_id: arxiv: - '2106.13185' isi: - '001024369000001' file: - access_level: open_access checksum: 2b45828d854a253b14bf7aa196ec55e9 content_type: application/pdf creator: dernst date_created: 2023-11-14T13:12:12Z date_updated: 2023-11-14T13:12:12Z file_id: '14535' file_name: 2023_ArchiveRationalMechAnalysis_Benedikter.pdf file_size: 851626 relation: main_file success: 1 file_date_updated: 2023-11-14T13:12:12Z has_accepted_license: '1' intvolume: ' 247' isi: 1 issue: '4' language: - iso: eng month: '08' 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 publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Correlation energy of a weakly interacting Fermi gas with large interaction potential tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 247 year: '2023' ... --- _id: '13226' abstract: - lang: eng text: We consider the ground state and the low-energy excited states of a system of N identical bosons with interactions in the mean-field scaling regime. For the ground state, we derive a weak Edgeworth expansion for the fluctuations of bounded one-body operators, which yields corrections to a central limit theorem to any order in 1/N−−√. For suitable excited states, we show that the limiting distribution is a polynomial times a normal distribution, and that higher-order corrections are given by an Edgeworth-type expansion. acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee for many constructive comments. L.B. gratefully acknowledges funding from the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111) and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen Access funding enabled and organized by Projekt DEAL." article_number: '77' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 - 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: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 2023;113(4). doi:10.1007/s11005-023-01698-4 apa: Bossmann, L., & Petrat, S. P. (2023). Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-023-01698-4 chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s11005-023-01698-4. ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field Bose gas,” Letters in Mathematical Physics, vol. 113, no. 4. Springer Nature, 2023. ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose gas. Letters in Mathematical Physics. 113(4), 77. mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field Bose Gas.” Letters in Mathematical Physics, vol. 113, no. 4, 77, Springer Nature, 2023, doi:10.1007/s11005-023-01698-4. short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023). date_created: 2023-07-16T22:01:08Z date_published: 2023-07-03T00:00:00Z date_updated: 2023-12-13T11:31:50Z day: '03' department: - _id: RoSe doi: 10.1007/s11005-023-01698-4 ec_funded: 1 external_id: arxiv: - '2208.00199' isi: - '001022878900002' intvolume: ' 113' isi: 1 issue: '4' language: - iso: eng month: '07' oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Weak Edgeworth expansion for the mean-field Bose gas type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 113 year: '2023' ... --- _id: '14192' abstract: - lang: eng text: For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling. acknowledgement: D.M. and K.M. thank Robert Seiringer for helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria). Financial support from the Agence Nationale de la Recherche (ANR) through the projects ANR-17-CE40-0016, ANR-17-CE40-0007-01, ANR-17-EURE-0002 (J.L.) and from the European Union’s Horizon 2020 research and innovation programme under the Maria Skłodowska-Curie grant agreement No. 665386 (K.M.) is gratefully acknowledged. article_number: '17' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Jonas full_name: Lampart, Jonas last_name: Lampart - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy citation: ama: Lampart J, Mitrouskas DJ, Mysliwy K. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 2023;26(3). doi:10.1007/s11040-023-09460-x apa: Lampart, J., Mitrouskas, D. J., & Mysliwy, K. (2023). On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-023-09460-x chicago: Lampart, Jonas, David Johannes Mitrouskas, and Krzysztof Mysliwy. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2023. https://doi.org/10.1007/s11040-023-09460-x. ieee: J. Lampart, D. J. Mitrouskas, and K. Mysliwy, “On the global minimum of the energy–momentum relation for the polaron,” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3. Springer Nature, 2023. ista: Lampart J, Mitrouskas DJ, Mysliwy K. 2023. On the global minimum of the energy–momentum relation for the polaron. Mathematical Physics, Analysis and Geometry. 26(3), 17. mla: Lampart, Jonas, et al. “On the Global Minimum of the Energy–Momentum Relation for the Polaron.” Mathematical Physics, Analysis and Geometry, vol. 26, no. 3, 17, Springer Nature, 2023, doi:10.1007/s11040-023-09460-x. short: J. Lampart, D.J. Mitrouskas, K. Mysliwy, Mathematical Physics, Analysis and Geometry 26 (2023). date_created: 2023-08-22T14:09:47Z date_published: 2023-07-26T00:00:00Z date_updated: 2023-12-13T12:16:19Z day: '26' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11040-023-09460-x external_id: arxiv: - '2206.14708' isi: - '001032992600001' file: - access_level: open_access checksum: f0941cc66cb3ed06a12ca4b7e356cfd6 content_type: application/pdf creator: dernst date_created: 2023-08-23T10:59:15Z date_updated: 2023-08-23T10:59:15Z file_id: '14225' file_name: 2023_MathPhysics_Lampart.pdf file_size: 317026 relation: main_file success: 1 file_date_updated: 2023-08-23T10:59:15Z has_accepted_license: '1' intvolume: ' 26' isi: 1 issue: '3' keyword: - Geometry and Topology - Mathematical Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version publication: Mathematical Physics, Analysis and Geometry publication_identifier: eissn: - 1572-9656 issn: - 1385-0172 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the global minimum of the energy–momentum relation for the polaron tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 26 year: '2023' ... --- _id: '14715' abstract: - lang: eng text: We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ. acknowledgement: We thank Lea Boßmann, Phan Thành Nam and Simone Rademacher for helpful remarks. P.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Grant No. SFB/TRR 352 “Mathematics of Many-Body Quantum Systems and Their Collective Phenomena.” article_number: '121901' article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Peter full_name: Pickl, Peter last_name: Pickl citation: ama: Mitrouskas DJ, Pickl P. Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. 2023;64(12). doi:10.1063/5.0172199 apa: Mitrouskas, D. J., & Pickl, P. (2023). Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0172199 chicago: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2023. https://doi.org/10.1063/5.0172199. ieee: D. J. Mitrouskas and P. Pickl, “Exponential decay of the number of excitations in the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 64, no. 12. AIP Publishing, 2023. ista: Mitrouskas DJ, Pickl P. 2023. Exponential decay of the number of excitations in the weakly interacting Bose gas. Journal of Mathematical Physics. 64(12), 121901. mla: Mitrouskas, David Johannes, and Peter Pickl. “Exponential Decay of the Number of Excitations in the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 64, no. 12, 121901, AIP Publishing, 2023, doi:10.1063/5.0172199. short: D.J. Mitrouskas, P. Pickl, Journal of Mathematical Physics 64 (2023). date_created: 2023-12-31T23:01:02Z date_published: 2023-12-01T00:00:00Z date_updated: 2024-01-02T08:51:28Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1063/5.0172199 external_id: arxiv: - '2307.11062' file: - access_level: open_access checksum: 66572f718a36465576cf0d6b3f7e01fc content_type: application/pdf creator: dernst date_created: 2024-01-02T08:45:07Z date_updated: 2024-01-02T08:45:07Z file_id: '14722' file_name: 2023_JourMathPhysics_Mitrouskas.pdf file_size: 4346922 relation: main_file success: 1 file_date_updated: 2024-01-02T08:45:07Z has_accepted_license: '1' intvolume: ' 64' issue: '12' language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Exponential decay of the number of excitations in the weakly interacting Bose 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 64 year: '2023' ... --- _id: '14854' abstract: - lang: eng text: "\r\nAbstract\r\nWe study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type." article_processing_charge: No article_type: original author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mitrouskas DJ, Seiringer R. Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. 2023;5(4):973-1008. doi:10.2140/paa.2023.5.973 apa: Mitrouskas, D. J., & Seiringer, R. (2023). Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2023.5.973 chicago: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/paa.2023.5.973. ieee: D. J. Mitrouskas and R. Seiringer, “Ubiquity of bound states for the strongly coupled polaron,” Pure and Applied Analysis, vol. 5, no. 4. Mathematical Sciences Publishers, pp. 973–1008, 2023. ista: Mitrouskas DJ, Seiringer R. 2023. Ubiquity of bound states for the strongly coupled polaron. Pure and Applied Analysis. 5(4), 973–1008. mla: Mitrouskas, David Johannes, and Robert Seiringer. “Ubiquity of Bound States for the Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 5, no. 4, Mathematical Sciences Publishers, 2023, pp. 973–1008, doi:10.2140/paa.2023.5.973. short: D.J. Mitrouskas, R. Seiringer, Pure and Applied Analysis 5 (2023) 973–1008. date_created: 2024-01-22T08:24:23Z date_published: 2023-12-15T00:00:00Z date_updated: 2024-01-23T12:55:12Z day: '15' department: - _id: RoSe doi: 10.2140/paa.2023.5.973 intvolume: ' 5' issue: '4' keyword: - General Medicine language: - iso: eng month: '12' oa_version: None page: 973-1008 publication: Pure and Applied Analysis publication_identifier: issn: - 2578-5885 - 2578-5893 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' status: public title: Ubiquity of bound states for the strongly coupled polaron type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2023' ... --- _id: '14254' abstract: - lang: eng text: In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality. acknowledgement: J.P.S. thanks the Institute of Science and Technology Austria for the hospitality and support during a visit where this work was done. J.P.S. was also partially supported by the VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH) (grant No. 10059). article_number: '110129' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jan Philip full_name: Solovej, Jan Philip last_name: Solovej citation: ama: Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 2023;285(10). doi:10.1016/j.jfa.2023.110129 apa: Seiringer, R., & Solovej, J. P. (2023). A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.110129 chicago: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110129. ieee: R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,” Journal of Functional Analysis, vol. 285, no. 10. Elsevier, 2023. ista: Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 285(10), 110129. mla: Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” Journal of Functional Analysis, vol. 285, no. 10, 110129, Elsevier, 2023, doi:10.1016/j.jfa.2023.110129. short: R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023). date_created: 2023-09-03T22:01:14Z date_published: 2023-11-15T00:00:00Z date_updated: 2024-01-30T14:17:23Z day: '15' ddc: - '510' department: - _id: RoSe doi: 10.1016/j.jfa.2023.110129 external_id: arxiv: - '2303.04504' isi: - '001071552300001' file: - access_level: open_access checksum: 28e424ad91be6219e9d321054ce3a412 content_type: application/pdf creator: dernst date_created: 2024-01-30T14:15:16Z date_updated: 2024-01-30T14:15:16Z file_id: '14915' file_name: 2023_JourFunctionalAnalysis_Seiringer.pdf file_size: 232934 relation: main_file success: 1 file_date_updated: 2024-01-30T14:15:16Z has_accepted_license: '1' intvolume: ' 285' isi: 1 issue: '10' language: - iso: eng month: '11' oa: 1 oa_version: Published Version publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: A simple approach to Lieb-Thirring type inequalities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 285 year: '2023' ... --- _id: '14992' abstract: - lang: eng text: In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and interaction energy that can be reached with all possible quantum states having a given density. We discuss two possible convex generalizations of this functional, corresponding to using mixed canonical and grand-canonical states, respectively. We present some recent works about the local density approximation, in which the functionals get replaced by purely local functionals constructed using the uniform electron gas energy per unit volume. We then review the known upper and lower bounds on the Levy–Lieb functionals. We start with the kinetic energy alone, then turn to the classical interaction alone, before we are able to put everything together. A later section is devoted to the Hohenberg–Kohn theorem and the role of many-body unique continuation in its proof. alternative_title: - Mathematics and Molecular Modeling article_processing_charge: No 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. Universal Functionals in Density Functional Theory. In: Cances E, Friesecke G, eds. Density Functional Theory. 1st ed. MAMOMO. Springer; 2023:115-182. doi:10.1007/978-3-031-22340-2_3' apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2023). Universal Functionals in Density Functional Theory. In E. Cances & G. Friesecke (Eds.), Density Functional Theory (1st ed., pp. 115–182). Springer. https://doi.org/10.1007/978-3-031-22340-2_3 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Universal Functionals in Density Functional Theory.” In Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st ed., 115–82. MAMOMO. Springer, 2023. https://doi.org/10.1007/978-3-031-22340-2_3. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Universal Functionals in Density Functional Theory,” in Density Functional Theory, 1st ed., E. Cances and G. Friesecke, Eds. Springer, 2023, pp. 115–182. ista: 'Lewin M, Lieb EH, Seiringer R. 2023.Universal Functionals in Density Functional Theory. In: Density Functional Theory. Mathematics and Molecular Modeling, , 115–182.' mla: Lewin, Mathieu, et al. “Universal Functionals in Density Functional Theory.” Density Functional Theory, edited by Eric Cances and Gero Friesecke, 1st ed., Springer, 2023, pp. 115–82, doi:10.1007/978-3-031-22340-2_3. short: M. Lewin, E.H. Lieb, R. Seiringer, in:, E. Cances, G. Friesecke (Eds.), Density Functional Theory, 1st ed., Springer, 2023, pp. 115–182. date_created: 2024-02-14T14:44:33Z date_published: 2023-07-19T00:00:00Z date_updated: 2024-02-20T08:33:06Z day: '19' department: - _id: RoSe doi: 10.1007/978-3-031-22340-2_3 edition: '1' editor: - first_name: Eric full_name: Cances, Eric last_name: Cances - first_name: Gero full_name: Friesecke, Gero last_name: Friesecke external_id: arxiv: - '1912.10424' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1912.10424 month: '07' oa: 1 oa_version: Preprint page: 115-182 publication: Density Functional Theory publication_identifier: eisbn: - '9783031223402' isbn: - '9783031223396' issn: - 3005-0286 publication_status: published publisher: Springer quality_controlled: '1' series_title: MAMOMO status: public title: Universal Functionals in Density Functional Theory type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2023' ... --- _id: '12276' abstract: - lang: eng text: Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model. acknowledgement: We thank A. A. Michailidis for insightful discussions. M.L. and M.S. acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 850899). D.A. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 864597) and by the Swiss National Science Foundation. The infinite TEBD simulations were performed using the ITensor library [67]. article_number: '030343' article_processing_charge: No article_type: original author: - first_name: Marko full_name: Ljubotina, Marko id: F75EE9BE-5C90-11EA-905D-16643DDC885E last_name: Ljubotina - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 - first_name: Dmitry A. full_name: Abanin, Dmitry A. last_name: Abanin - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 citation: ama: Ljubotina M, Roos B, Abanin DA, Serbyn M. Optimal steering of matrix product states and quantum many-body scars. PRX Quantum. 2022;3(3). doi:10.1103/prxquantum.3.030343 apa: Ljubotina, M., Roos, B., Abanin, D. A., & Serbyn, M. (2022). Optimal steering of matrix product states and quantum many-body scars. PRX Quantum. American Physical Society. https://doi.org/10.1103/prxquantum.3.030343 chicago: Ljubotina, Marko, Barbara Roos, Dmitry A. Abanin, and Maksym Serbyn. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” PRX Quantum. American Physical Society, 2022. https://doi.org/10.1103/prxquantum.3.030343. ieee: M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, “Optimal steering of matrix product states and quantum many-body scars,” PRX Quantum, vol. 3, no. 3. American Physical Society, 2022. ista: Ljubotina M, Roos B, Abanin DA, Serbyn M. 2022. Optimal steering of matrix product states and quantum many-body scars. PRX Quantum. 3(3), 030343. mla: Ljubotina, Marko, et al. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” PRX Quantum, vol. 3, no. 3, 030343, American Physical Society, 2022, doi:10.1103/prxquantum.3.030343. short: M. Ljubotina, B. Roos, D.A. Abanin, M. Serbyn, PRX Quantum 3 (2022). date_created: 2023-01-16T10:01:56Z date_published: 2022-09-23T00:00:00Z date_updated: 2023-01-30T11:05:23Z day: '23' ddc: - '530' department: - _id: MaSe - _id: RoSe doi: 10.1103/prxquantum.3.030343 ec_funded: 1 external_id: arxiv: - '2204.02899' file: - access_level: open_access checksum: ef8f0a1b5a019b3958009162de0fa4c3 content_type: application/pdf creator: dernst date_created: 2023-01-30T11:02:50Z date_updated: 2023-01-30T11:02:50Z file_id: '12457' file_name: 2022_PRXQuantum_Ljubotina.pdf file_size: 7661905 relation: main_file success: 1 file_date_updated: 2023-01-30T11:02:50Z has_accepted_license: '1' intvolume: ' 3' issue: '3' keyword: - General Medicine language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 23841C26-32DE-11EA-91FC-C7463DDC885E call_identifier: H2020 grant_number: '850899' name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control' publication: PRX Quantum publication_identifier: eissn: - 2691-3399 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Optimal steering of matrix product states and quantum many-body scars tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2022' ... --- _id: '11783' abstract: - lang: eng text: We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix. acknowledgement: "The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged." article_number: '061102' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 citation: ama: Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983 apa: Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983 chicago: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983. ieee: L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing, 2022. ista: Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102. mla: Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:10.1063/5.0089983. short: L. Bossmann, Journal of Mathematical Physics 63 (2022). date_created: 2022-08-11T06:37:52Z date_published: 2022-06-10T00:00:00Z date_updated: 2023-08-03T12:46:28Z day: '10' ddc: - '530' department: - _id: RoSe doi: 10.1063/5.0089983 ec_funded: 1 external_id: arxiv: - '2203.00730' isi: - '000809648100002' file: - access_level: open_access checksum: d0d32c338c1896680174be88c70968fa content_type: application/pdf creator: dernst date_created: 2022-08-11T07:03:02Z date_updated: 2022-08-11T07:03:02Z file_id: '11784' file_name: 2022_JourMathPhysics_Bossmann.pdf file_size: 5957888 relation: main_file success: 1 file_date_updated: 2022-08-11T07:03:02Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '6' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Low-energy spectrum and dynamics of the weakly interacting Bose 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: 63 year: '2022' ... --- _id: '11917' abstract: - lang: eng text: We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order. acknowledgement: "The authors thank Gérard Ben Arous for pointing out the question of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding provided by IST Austria." article_number: '9' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4 apa: Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02940-4 chicago: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4. ieee: S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly interacting bosons,” Journal of Statistical Physics, vol. 188. Springer Nature, 2022. ista: Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9. mla: Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188, 9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4. short: S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022). date_created: 2022-08-18T07:23:26Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-08-03T12:55:58Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s10955-022-02940-4 ec_funded: 1 external_id: isi: - '000805175000001' file: - access_level: open_access checksum: 44418cb44f07fa21ed3907f85abf7f39 content_type: application/pdf creator: dernst date_created: 2022-08-18T08:09:00Z date_updated: 2022-08-18T08:09:00Z file_id: '11922' file_name: 2022_JournalStatisticalPhysics_Rademacher.pdf file_size: 483481 relation: main_file success: 1 file_date_updated: 2022-08-18T08:09:00Z has_accepted_license: '1' intvolume: ' 188' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' 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: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Large deviation estimates for weakly interacting bosons 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: 188 year: '2022' ... --- _id: '12083' abstract: - lang: eng text: We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem. acknowledgement: S.R. would like to thank Robert Seiringer and Benedikt Stufler for helpful discussions. Funding from the European Union’s Horizon 2020 Research and Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged. article_number: '081902' article_processing_charge: No article_type: original author: - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 citation: ama: Rademacher SAE. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 2022;63(8). doi:10.1063/5.0086712 apa: Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0086712 chicago: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0086712. ieee: S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” Journal of Mathematical Physics, vol. 63, no. 8. AIP Publishing, 2022. ista: Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 63(8), 081902. mla: Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics, vol. 63, no. 8, 081902, AIP Publishing, 2022, doi:10.1063/5.0086712. short: S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022). date_created: 2022-09-11T22:01:56Z date_published: 2022-08-25T00:00:00Z date_updated: 2023-08-03T13:57:19Z day: '25' ddc: - '510' department: - _id: RoSe doi: 10.1063/5.0086712 ec_funded: 1 external_id: arxiv: - '2112.04817' isi: - '000844402500001' file: - access_level: open_access checksum: e6fb0cf3f0327739c5e69a2cfc4020eb content_type: application/pdf creator: dernst date_created: 2022-09-12T07:35:34Z date_updated: 2022-09-12T07:35:34Z file_id: '12089' file_name: 2022_JourMathPhysics_Rademacher.pdf file_size: 4552261 relation: main_file success: 1 file_date_updated: 2022-09-12T07:35:34Z has_accepted_license: '1' intvolume: ' 63' isi: 1 issue: '8' language: - iso: eng month: '08' 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: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Journal of Mathematical Physics publication_identifier: issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Dependent random variables in quantum dynamics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 63 year: '2022' ... --- _id: '12390' abstract: - lang: eng text: "The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that\r\nis broken on the level of the corresponding effective theory. In particular we are going to\r\ninvestigate translation-invariant Bose gases in the mean field limit, effectively described by\r\nthe Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed by the Pekar functional. The latter is a model describing the interaction between a\r\ncharged particle and the optical modes of a polar crystal. Regarding the former, we assume in\r\naddition that the particles in the gas are unconfined, and typically we will consider particles\r\nthat are subject to an attractive interaction. In both cases the ground state energy of the\r\nHamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe contrary there exists a whole invariant orbit of minimizers for the corresponding effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken symmetry of the effective\r\ntheory, make the study significantly more involved and it is the content of this thesis to\r\ndevelop a frameworks which allows for a systematic way to circumvent these issues.\r\nIt is a well-established result that the ground state energy of Bose gases in the mean field limit,\r\nas well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is\r\nto leading order given by the minimal energy of the corresponding effective theory. As part\r\nof this thesis we identify the sub-leading term in the expansion of the ground state energy,\r\nwhich can be interpreted as the quantum correction to the classical energy, since the effective\r\ntheories under consideration can be seen as classical counterparts.\r\nWe are further going to establish an asymptotic expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic expression agrees with the energy-momentum relation of a free particle having\r\nan effectively increased mass, and we find that this effectively increased mass agrees with the\r\nconjectured value in the physics literature.\r\nIn addition we will discuss two unrelated papers written by the author during his stay at ISTA\r\nin the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe second one provides a classification of those vector fields defined on a given manifold\r\nthat can be written as the gradient of a given functional with respect to a suitable metric,\r\nprovided that some mild smoothness assumptions hold. This classification is subsequently\r\nused to identify those quantum Markov semigroups that can be written as a gradient flow of\r\nthe relative entropy.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 citation: ama: Brooks M. Translation-invariant quantum systems with effectively broken symmetry. 2022. doi:10.15479/at:ista:12390 apa: Brooks, M. (2022). Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12390 chicago: Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively Broken Symmetry.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12390. ieee: M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022. ista: Brooks M. 2022. Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria. mla: Brooks, Morris. Translation-Invariant Quantum Systems with Effectively Broken Symmetry. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12390. short: M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022. date_created: 2023-01-26T10:00:42Z date_published: 2022-12-15T00:00:00Z date_updated: 2023-08-07T13:32:09Z day: '15' ddc: - '500' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:12390 ec_funded: 1 file: - access_level: open_access checksum: b31460e937f33b557abb40ebef02b567 content_type: application/pdf creator: cchlebak date_created: 2023-01-26T10:02:34Z date_updated: 2023-01-26T10:02:34Z file_id: '12391' file_name: Brooks_Thesis.pdf file_size: 3095225 relation: main_file success: 1 - access_level: closed checksum: 9751869fa5e7981588ad4228f4fd4bd6 content_type: application/octet-stream creator: cchlebak date_created: 2023-01-26T10:02:42Z date_updated: 2023-01-26T10:02:42Z file_id: '12392' file_name: Brooks_Thesis.tex file_size: 809842 relation: source_file file_date_updated: 2023-01-26T10:02:42Z has_accepted_license: '1' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: '196' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9005' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Translation-invariant quantum systems with effectively broken symmetry tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '11732' abstract: - lang: eng text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)" article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9 apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9 chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9. ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022. ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5. mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9. short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022). date_created: 2022-08-05T11:36:56Z date_published: 2022-07-29T00:00:00Z date_updated: 2023-09-05T14:57:49Z day: '29' ddc: - '530' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1007/s10955-022-02965-9 ec_funded: 1 external_id: isi: - '000833007200002' file: - access_level: open_access checksum: b398c4dbf65f71d417981d6e366427e9 content_type: application/pdf creator: dernst date_created: 2022-08-08T07:36:34Z date_updated: 2022-08-08T07:36:34Z file_id: '11746' file_name: 2022_JourStatisticalPhysics_Henheik.pdf file_size: 419563 relation: main_file success: 1 file_date_updated: 2022-08-08T07:36:34Z has_accepted_license: '1' intvolume: ' 189' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS energy gap at high density 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: 189 year: '2022' ... --- _id: '12246' abstract: - lang: eng text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy. acknowledgement: We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done. article_number: '92' 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. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5 apa: Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-022-01584-5 chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5. ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” Letters in Mathematical Physics, vol. 112, no. 5. Springer Nature, 2022. ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92. mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer Nature, 2022, doi:10.1007/s11005-022-01584-5. short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022). date_created: 2023-01-16T09:53:54Z date_published: 2022-09-15T00:00:00Z date_updated: 2023-09-05T15:17:34Z day: '15' department: - _id: RoSe doi: 10.1007/s11005-022-01584-5 ec_funded: 1 external_id: arxiv: - '2203.12473' isi: - '000854762600001' intvolume: ' 112' isi: 1 issue: '5' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2203.12473 month: '09' 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: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Improved Lieb–Oxford bound on the indirect and exchange energies type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 112 year: '2022' ... --- _id: '11473' abstract: - lang: eng text: "The polaron model is a basic model of quantum field theory describing a single particle\r\ninteracting with a bosonic field. It arises in many physical contexts. We are mostly concerned\r\nwith models applicable in the context of an impurity atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving in polar crystals.\r\nThe model has a simple structure in which the interaction of the particle with the field is given\r\nby a term linear in the field’s creation and annihilation operators. In this work, we investigate\r\nthe properties of this model by providing rigorous estimates on various energies relevant to the\r\nproblem. The estimates are obtained, for the most part, by suitable operator techniques which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe first application of these techniques is to derive the polaron model rigorously from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective theory for this problem.\r\nIn the second part, we investigate rigorously the ground state of the model at fixed momentum\r\nand for large values of the coupling constant. Qualitatively, the system is expected to display\r\na transition from the quasi-particle behavior at small momenta, where the dispersion relation\r\nis parabolic and the particle moves through the medium dragging along a cloud of phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates and emits free phonons.\r\nAt the same time, in the strong coupling regime, the bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst studied by Landau and Pekar in the 1940s. For polaron models with regularized form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove\r\nthat for a large window of momenta below the radiation threshold, the energy-momentum\r\nrelation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is\r\nof the optical type and the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe regular case, this requires the inclusion of the quantum fluctuations of the phonon field,\r\nwhich makes the problem considerably more difficult.\r\nThe results are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na proof of the divergence of the effective mass with the coupling constant for a wide class of\r\npolaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model\r\nand the application of the techniques used for its removal for the energy estimates.\r\n" acknowledged_ssus: - _id: SSU alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy citation: ama: 'Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. 2022. doi:10.15479/at:ista:11473' apa: 'Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473' chicago: 'Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.' ieee: 'K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy estimates,” Institute of Science and Technology Austria, 2022.' ista: 'Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria.' mla: 'Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473.' short: 'K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates, Institute of Science and Technology Austria, 2022.' date_created: 2022-06-30T12:15:03Z date_published: 2022-07-01T00:00:00Z date_updated: 2023-09-07T13:43:52Z day: '01' ddc: - '515' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:11473 ec_funded: 1 file: - access_level: open_access checksum: 7970714a20a6052f75fb27a6c3e9976e content_type: application/pdf creator: kmysliwy date_created: 2022-07-05T08:12:56Z date_updated: 2022-07-05T08:12:56Z file_id: '11486' file_name: thes1_no_isbn_2_1b.pdf file_size: 1830973 relation: main_file success: 1 - access_level: closed checksum: 647a2011fdf56277096c9350fefe1097 content_type: application/zip creator: kmysliwy date_created: 2022-07-05T08:15:52Z date_updated: 2022-07-05T08:17:12Z file_id: '11487' file_name: thes_source.zip file_size: 5831060 relation: source_file file_date_updated: 2022-07-05T08:17:12Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '138' project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '10564' relation: part_of_dissertation status: public - id: '8705' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: 'Polarons in Bose gases and polar crystals: Some rigorous energy estimates' type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2022' ... --- _id: '10564' abstract: - lang: eng text: We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass. acknowledgement: Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant Agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.) is gratefully acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria). article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Krzysztof full_name: Mysliwy, Krzysztof id: 316457FC-F248-11E8-B48F-1D18A9856A87 last_name: Mysliwy - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mysliwy K, Seiringer R. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w apa: Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w chicago: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w. ieee: K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer Nature, 2022. ista: Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5. mla: Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5, Springer Nature, 2022, doi:10.1007/s10955-021-02851-w. short: K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022). date_created: 2021-12-19T23:01:32Z date_published: 2022-01-01T00:00:00Z date_updated: 2023-09-07T13:43:51Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s10955-021-02851-w ec_funded: 1 external_id: arxiv: - '2106.09328' isi: - '000726275600001' file: - access_level: open_access checksum: da03f6d293c4b9802091bce9471b1d29 content_type: application/pdf creator: cchlebak date_created: 2022-02-02T14:24:41Z date_updated: 2022-02-02T14:24:41Z file_id: '10716' file_name: 2022_JournalStatPhys_Myśliwy.pdf file_size: 434957 relation: main_file success: 1 file_date_updated: 2022-02-02T14:24:41Z has_accepted_license: '1' intvolume: ' 186' isi: 1 issue: '1' language: - iso: eng month: '01' 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: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '11473' relation: dissertation_contains status: public scopus_import: '1' status: public title: Polaron models with regular interactions at strong coupling 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: 186 year: '2022' ... --- _id: '10850' abstract: - lang: eng text: "We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1." acknowledgement: We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged. article_number: '109455' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Barbara full_name: Roos, Barbara id: 5DA90512-D80F-11E9-8994-2E2EE6697425 last_name: Roos orcid: 0000-0002-9071-5880 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455 apa: Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455 chicago: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455. ieee: B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022. ista: Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455. mla: Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455, Elsevier, 2022, doi:10.1016/j.jfa.2022.109455. short: B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022). date_created: 2022-03-16T08:41:53Z date_published: 2022-06-15T00:00:00Z date_updated: 2023-10-27T10:37:29Z day: '15' ddc: - '510' department: - _id: GradSch - _id: RoSe doi: 10.1016/j.jfa.2022.109455 ec_funded: 1 external_id: arxiv: - '2105.04874' isi: - '000795160200009' file: - access_level: open_access checksum: 63efcefaa1f2717244ef5407bd564426 content_type: application/pdf creator: dernst date_created: 2022-08-02T10:37:55Z date_updated: 2022-08-02T10:37:55Z file_id: '11720' file_name: 2022_JourFunctionalAnalysis_Roos.pdf file_size: 631391 relation: main_file success: 1 file_date_updated: 2022-08-02T10:37:55Z has_accepted_license: '1' intvolume: ' 282' isi: 1 issue: '12' keyword: - Analysis language: - iso: eng month: '06' 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 publication: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' related_material: record: - id: '14374' relation: dissertation_contains status: public scopus_import: '1' status: public title: Two-particle bound states at interfaces and corners 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: 282 year: '2022' ... --- _id: '10755' abstract: - lang: eng text: We provide a definition of the effective mass for the classical polaron described by the Landau–Pekar (LP) equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by LP (1948 J. Exp. Theor. Phys. 18 419–423). acknowledgement: "We thank Herbert Spohn for helpful comments. Funding from the European Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (SR) is\r\ngratefully acknowledged." article_number: '015201' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 2022;55(1). doi:10.1088/1751-8121/ac3947' apa: 'Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947' chicago: 'Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947.' ieee: 'D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.' ista: 'Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 55(1), 015201.' mla: 'Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.' short: 'D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022).' date_created: 2022-02-13T23:01:35Z date_published: 2022-01-19T00:00:00Z date_updated: 2024-03-06T12:30:44Z day: '19' ddc: - '510' department: - _id: RoSe doi: 10.1088/1751-8121/ac3947 ec_funded: 1 external_id: arxiv: - '2107.03720' file: - access_level: open_access checksum: 0875e562705563053d6dd98fba4d8578 content_type: application/pdf creator: dernst date_created: 2022-02-14T08:20:19Z date_updated: 2022-02-14T08:20:19Z file_id: '10757' file_name: 2022_JournalPhysicsA_Feliciangeli.pdf file_size: 1132380 relation: main_file success: 1 file_date_updated: 2022-02-14T08:20:19Z has_accepted_license: '1' intvolume: ' 55' issue: '1' language: - iso: eng month: '01' 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: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 'Journal of Physics A: Mathematical and Theoretical' publication_identifier: eissn: - 1751-8121 issn: - 1751-8113 publication_status: published publisher: IOP Publishing quality_controlled: '1' related_material: record: - id: '9791' relation: earlier_version status: public scopus_import: '1' status: public title: The effective mass problem for the Landau-Pekar equations tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2022' ... --- _id: '10585' abstract: - lang: eng text: Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle acknowledgement: D. Lundholm acknowledges financial support from the Göran Gustafsson Foundation (grant no. 1804). article_number: '106' article_processing_charge: Yes article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: Douglas full_name: Lundholm, Douglas last_name: Lundholm - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 citation: ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 2021;9(4). doi:10.3390/atoms9040106 apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Emergence of anyons on the two-sphere in molecular impurities. Atoms. MDPI. https://doi.org/10.3390/atoms9040106 chicago: Brooks, Morris, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms. MDPI, 2021. https://doi.org/10.3390/atoms9040106. ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Emergence of anyons on the two-sphere in molecular impurities,” Atoms, vol. 9, no. 4. MDPI, 2021. ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 9(4), 106. mla: Brooks, Morris, et al. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms, vol. 9, no. 4, 106, MDPI, 2021, doi:10.3390/atoms9040106. short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Atoms 9 (2021). date_created: 2022-01-02T23:01:33Z date_published: 2021-12-02T00:00:00Z date_updated: 2023-06-15T14:51:49Z day: '02' ddc: - '530' department: - _id: MiLe - _id: RoSe doi: 10.3390/atoms9040106 external_id: arxiv: - '2108.06966' file: - access_level: open_access checksum: d0e44b95f36c9e06724f66832af0f8c3 content_type: application/pdf creator: alisjak date_created: 2022-01-03T10:15:05Z date_updated: 2022-01-03T10:15:05Z file_id: '10592' file_name: 2021_Atoms_Brooks.pdf file_size: 303070 relation: main_file success: 1 file_date_updated: 2022-01-03T10:15:05Z has_accepted_license: '1' intvolume: ' 9' issue: '4' keyword: - anyons - quasiparticles - Quantum Hall Effect - topological states of matter language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: Atoms publication_identifier: eissn: - 2218-2004 publication_status: published publisher: MDPI quality_controlled: '1' scopus_import: '1' status: public title: Emergence of anyons on the two-sphere in molecular impurities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2021' ... --- _id: '7685' abstract: - lang: eng text: We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein. article_number: '2060006' article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Boccato, Chiara id: 342E7E22-F248-11E8-B48F-1D18A9856A87 last_name: Boccato citation: ama: Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/S0129055X20600065 apa: Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. World Scientific. https://doi.org/10.1142/S0129055X20600065 chicago: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” Reviews in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/S0129055X20600065. ieee: C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021. ista: Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime. Reviews in Mathematical Physics. 33(1), 2060006. mla: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii Regime.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060006, World Scientific, 2021, doi:10.1142/S0129055X20600065. short: C. Boccato, Reviews in Mathematical Physics 33 (2021). date_created: 2020-04-26T22:00:45Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-08-04T10:50:13Z day: '01' department: - _id: RoSe doi: 10.1142/S0129055X20600065 ec_funded: 1 external_id: arxiv: - '2001.00497' isi: - '000613313200007' intvolume: ' 33' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2001.00497 month: '01' 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: Reviews in Mathematical Physics publication_identifier: issn: - 0129-055X publication_status: published publisher: World Scientific quality_controlled: '1' scopus_import: '1' status: public title: The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 33 year: '2021' ... --- _id: '8603' abstract: - lang: eng text: We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem. acknowledgement: Partial support through National Science Foundation GrantDMS-1363432 (R.L.F.) and the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo 694227; R.S.), is acknowledged. Open access funding enabled and organizedby Projekt DEAL. article_processing_charge: No article_type: original author: - first_name: Rupert full_name: Frank, Rupert last_name: Frank - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Frank R, Seiringer R. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. 2021;74(3):544-588. doi:10.1002/cpa.21944 apa: Frank, R., & Seiringer, R. (2021). Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21944 chicago: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics. Wiley, 2021. https://doi.org/10.1002/cpa.21944. ieee: R. Frank and R. Seiringer, “Quantum corrections to the Pekar asymptotics of a strongly coupled polaron,” Communications on Pure and Applied Mathematics, vol. 74, no. 3. Wiley, pp. 544–588, 2021. ista: Frank R, Seiringer R. 2021. Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Communications on Pure and Applied Mathematics. 74(3), 544–588. mla: Frank, Rupert, and Robert Seiringer. “Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron.” Communications on Pure and Applied Mathematics, vol. 74, no. 3, Wiley, 2021, pp. 544–88, doi:10.1002/cpa.21944. short: R. Frank, R. Seiringer, Communications on Pure and Applied Mathematics 74 (2021) 544–588. date_created: 2020-10-04T22:01:37Z date_published: 2021-03-01T00:00:00Z date_updated: 2023-08-04T11:02:16Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1002/cpa.21944 ec_funded: 1 external_id: isi: - '000572991500001' file: - access_level: open_access checksum: 5f665ffa6e6dd958aec5c3040cbcfa84 content_type: application/pdf creator: dernst date_created: 2021-03-11T10:03:30Z date_updated: 2021-03-11T10:03:30Z file_id: '9236' file_name: 2021_CommPureApplMath_Frank.pdf file_size: 334987 relation: main_file success: 1 file_date_updated: 2021-03-11T10:03:30Z has_accepted_license: '1' intvolume: ' 74' isi: 1 issue: '3' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 544-588 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Communications on Pure and Applied Mathematics publication_identifier: eissn: - '10970312' issn: - '00103640' publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Quantum corrections to the Pekar asymptotics of a strongly coupled polaron 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: 74 year: '2021' ... --- _id: '9005' abstract: - lang: eng text: Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field. acknowledgement: "We are grateful to A. Ghazaryan for valuable discussions and also thank the anonymous referees for comments. D.L. acknowledges financial support from the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully acknowledges financial support\r\nby the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770)." article_number: '015301' article_processing_charge: No article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: D. full_name: Lundholm, D. last_name: Lundholm - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 citation: ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301 apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301 chicago: Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301. ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities as a realization of anyons on the two-sphere,” Physical Review Letters, vol. 126, no. 1. American Physical Society, 2021. ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 126(1), 015301. mla: Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301. short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters 126 (2021). date_created: 2021-01-17T23:01:10Z date_published: 2021-01-08T00:00:00Z date_updated: 2023-08-07T13:32:10Z day: '08' department: - _id: MiLe - _id: RoSe doi: 10.1103/PhysRevLett.126.015301 ec_funded: 1 external_id: arxiv: - '2009.05948' isi: - '000606325000003' intvolume: ' 126' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2009.05948 month: '01' oa: 1 oa_version: Preprint project: - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' publication: Physical Review Letters publication_identifier: eissn: - '10797114' issn: - '00319007' publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/ record: - id: '12390' relation: dissertation_contains status: public scopus_import: '1' status: public title: Molecular impurities as a realization of anyons on the two-sphere type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 126 year: '2021' ... --- _id: '9246' abstract: - lang: eng text: We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order. acknowledgement: "Financial support by the European Research Council (ERC) under the\r\nEuropean Union’s Horizon 2020 research and innovation programme (Grant Agreement\r\nNo 694227; N.L and R.S.), the SNSF Eccellenza Project PCEFP2 181153 (N.L) and the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research TrainingGroup 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. N.L.\r\ngratefully acknowledges support from the NCCRSwissMAP and would like to thank Simone\r\nRademacher and Benjamin Schlein for interesting discussions about the time-evolution of\r\nthe polaron at strong coupling. D.M. thanks Marcel Griesemer and Andreas Wünsch for\r\nextensive discussions about the Fröhlich polaron." article_processing_charge: No 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: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Leopold NK, Mitrouskas DJ, Seiringer R. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 2021;240:383-417. doi:10.1007/s00205-021-01616-9 apa: Leopold, N. K., Mitrouskas, D. J., & Seiringer, R. (2021). Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01616-9 chicago: Leopold, Nikolai K, David Johannes Mitrouskas, and Robert Seiringer. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01616-9. ieee: N. K. Leopold, D. J. Mitrouskas, and R. Seiringer, “Derivation of the Landau–Pekar equations in a many-body mean-field limit,” Archive for Rational Mechanics and Analysis, vol. 240. Springer Nature, pp. 383–417, 2021. ista: Leopold NK, Mitrouskas DJ, Seiringer R. 2021. Derivation of the Landau–Pekar equations in a many-body mean-field limit. Archive for Rational Mechanics and Analysis. 240, 383–417. mla: Leopold, Nikolai K., et al. “Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit.” Archive for Rational Mechanics and Analysis, vol. 240, Springer Nature, 2021, pp. 383–417, doi:10.1007/s00205-021-01616-9. short: N.K. Leopold, D.J. Mitrouskas, R. Seiringer, Archive for Rational Mechanics and Analysis 240 (2021) 383–417. date_created: 2021-03-14T23:01:34Z date_published: 2021-02-26T00:00:00Z date_updated: 2023-08-07T14:12:27Z day: '26' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00205-021-01616-9 ec_funded: 1 external_id: arxiv: - '2001.03993' isi: - '000622226200001' file: - access_level: open_access checksum: 23449e44dc5132501a5c86e70638800f content_type: application/pdf creator: dernst date_created: 2021-03-22T08:31:29Z date_updated: 2021-03-22T08:31:29Z file_id: '9270' file_name: 2021_ArchRationalMechAnal_Leopold.pdf file_size: 558006 relation: main_file success: 1 file_date_updated: 2021-03-22T08:31:29Z has_accepted_license: '1' intvolume: ' 240' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 383-417 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - '14320673' issn: - '00039527' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Derivation of the Landau–Pekar equations in a many-body mean-field limit tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 240 year: '2021' ... --- _id: '9256' abstract: - lang: eng text: We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin S≥1/2. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature. acknowledgement: "The work of MN was supported by the National Science Centre (NCN) Project Nr. 2016/21/D/ST1/02430. The work of RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '31' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Napiórkowski MM, Seiringer R. Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. 2021;111(2). doi:10.1007/s11005-021-01375-4 apa: Napiórkowski, M. M., & Seiringer, R. (2021). Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01375-4 chicago: Napiórkowski, Marcin M, and Robert Seiringer. “Free Energy Asymptotics of the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01375-4. ieee: M. M. Napiórkowski and R. Seiringer, “Free energy asymptotics of the quantum Heisenberg spin chain,” Letters in Mathematical Physics, vol. 111, no. 2. Springer Nature, 2021. ista: Napiórkowski MM, Seiringer R. 2021. Free energy asymptotics of the quantum Heisenberg spin chain. Letters in Mathematical Physics. 111(2), 31. mla: Napiórkowski, Marcin M., and Robert Seiringer. “Free Energy Asymptotics of the Quantum Heisenberg Spin Chain.” Letters in Mathematical Physics, vol. 111, no. 2, 31, Springer Nature, 2021, doi:10.1007/s11005-021-01375-4. short: M.M. Napiórkowski, R. Seiringer, Letters in Mathematical Physics 111 (2021). date_created: 2021-03-21T23:01:19Z date_published: 2021-03-09T00:00:00Z date_updated: 2023-08-07T14:17:00Z day: '09' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-021-01375-4 external_id: isi: - '000626837400001' file: - access_level: open_access checksum: 687fef1525789c0950de90468dd81604 content_type: application/pdf creator: dernst date_created: 2021-03-22T11:01:09Z date_updated: 2021-03-22T11:01:09Z file_id: '9273' file_name: 2021_LettersMathPhysics_Napiorkowski.pdf file_size: 397962 relation: main_file success: 1 file_date_updated: 2021-03-22T11:01:09Z has_accepted_license: '1' intvolume: ' 111' isi: 1 issue: '2' language: - iso: eng month: '03' oa: 1 oa_version: Published Version publication: Letters in Mathematical Physics publication_identifier: eissn: - '15730530' issn: - '03779017' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Free energy asymptotics of the quantum Heisenberg spin chain 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: 111 year: '2021' ... --- _id: '9318' abstract: - lang: eng text: We consider a system of N bosons in the mean-field scaling regime for a class of interactions including the repulsive Coulomb potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N. acknowledgement: The first author gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 754411. The third author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694227). article_number: e28 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Lea full_name: Bossmann, Lea id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425 last_name: Bossmann orcid: 0000-0002-6854-1343 - first_name: Sören P full_name: Petrat, Sören P id: 40AC02DC-F248-11E8-B48F-1D18A9856A87 last_name: Petrat orcid: 0000-0002-9166-5889 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Bossmann L, Petrat SP, Seiringer R. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.22 apa: Bossmann, L., Petrat, S. P., & Seiringer, R. (2021). Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.22 chicago: Bossmann, Lea, Sören P Petrat, and Robert Seiringer. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.22. ieee: L. Bossmann, S. P. Petrat, and R. Seiringer, “Asymptotic expansion of low-energy excitations for weakly interacting bosons,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021. ista: Bossmann L, Petrat SP, Seiringer R. 2021. Asymptotic expansion of low-energy excitations for weakly interacting bosons. Forum of Mathematics, Sigma. 9, e28. mla: Bossmann, Lea, et al. “Asymptotic Expansion of Low-Energy Excitations for Weakly Interacting Bosons.” Forum of Mathematics, Sigma, vol. 9, e28, Cambridge University Press, 2021, doi:10.1017/fms.2021.22. short: L. Bossmann, S.P. Petrat, R. Seiringer, Forum of Mathematics, Sigma 9 (2021). date_created: 2021-04-11T22:01:15Z date_published: 2021-03-26T00:00:00Z date_updated: 2023-08-07T14:35:06Z day: '26' ddc: - '510' department: - _id: RoSe doi: 10.1017/fms.2021.22 ec_funded: 1 external_id: isi: - '000634006900001' file: - access_level: open_access checksum: 17a3e6786d1e930cf0c14a880a6d7e92 content_type: application/pdf creator: dernst date_created: 2021-04-12T07:15:58Z date_updated: 2021-04-12T07:15:58Z file_id: '9319' file_name: 2021_ForumMath_Bossmann.pdf file_size: 883851 relation: main_file success: 1 file_date_updated: 2021-04-12T07:15:58Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Asymptotic expansion of low-energy excitations for weakly interacting bosons 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: 9 year: '2021' ... --- _id: '9333' abstract: - lang: eng text: We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation. acknowledgement: 'I thank Marcel Griesemer for many interesting discussions about the Fröhlich polaron and also for valuable comments on this manuscript. Helpful discussions with Nikolai Leopold and Robert Seiringer are also gratefully acknowledged. This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral Theory and Dynamics of Quantum Systems. Open Access funding enabled and organized by Projekt DEAL.' article_number: '45' article_processing_charge: No article_type: original author: - first_name: David Johannes full_name: Mitrouskas, David Johannes id: cbddacee-2b11-11eb-a02e-a2e14d04e52d last_name: Mitrouskas citation: ama: Mitrouskas DJ. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-021-01380-7 apa: Mitrouskas, D. J. (2021). A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01380-7 chicago: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-021-01380-7. ieee: D. J. Mitrouskas, “A note on the Fröhlich dynamics in the strong coupling limit,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021. ista: Mitrouskas DJ. 2021. A note on the Fröhlich dynamics in the strong coupling limit. Letters in Mathematical Physics. 111, 45. mla: Mitrouskas, David Johannes. “A Note on the Fröhlich Dynamics in the Strong Coupling Limit.” Letters in Mathematical Physics, vol. 111, 45, Springer Nature, 2021, doi:10.1007/s11005-021-01380-7. short: D.J. Mitrouskas, Letters in Mathematical Physics 111 (2021). date_created: 2021-04-18T22:01:41Z date_published: 2021-04-05T00:00:00Z date_updated: 2023-08-08T13:09:28Z day: '05' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-021-01380-7 external_id: isi: - '000637359300002' file: - access_level: open_access checksum: be56c0845a43c0c5c772ee0b5053f7d7 content_type: application/pdf creator: dernst date_created: 2021-04-19T10:40:01Z date_updated: 2021-04-19T10:40:01Z file_id: '9341' file_name: 2021_LettersMathPhysics_Mitrouskas.pdf file_size: 438084 relation: main_file success: 1 file_date_updated: 2021-04-19T10:40:01Z has_accepted_license: '1' intvolume: ' 111' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Letters in Mathematical Physics publication_identifier: eissn: - '15730530' issn: - '03779017' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A note on the Fröhlich dynamics in the strong coupling limit tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 111 year: '2021' ... --- _id: '9351' abstract: - lang: eng text: 'We consider the many-body quantum evolution of a factorized initial data, in the mean-field regime. We show that fluctuations around the limiting Hartree dynamics satisfy large deviation estimates that are consistent with central limit theorems that have been established in the last years. ' acknowledgement: The authors gratefully acknowledge Gérard Ben Arous for suggesting this kind of result. K.L.K. was partially supported by NSF CAREER Award DMS-125479 and a Simons Sabbatical Fellowship. S.R. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. B. S. gratefully acknowledges partial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose–Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS. Funding Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Kay full_name: Kirkpatrick, Kay last_name: Kirkpatrick - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein citation: ama: Kirkpatrick K, Rademacher SAE, Schlein B. A large deviation principle in many-body quantum dynamics. Annales Henri Poincare. 2021;22:2595-2618. doi:10.1007/s00023-021-01044-1 apa: Kirkpatrick, K., Rademacher, S. A. E., & Schlein, B. (2021). A large deviation principle in many-body quantum dynamics. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-021-01044-1 chicago: Kirkpatrick, Kay, Simone Anna Elvira Rademacher, and Benjamin Schlein. “A Large Deviation Principle in Many-Body Quantum Dynamics.” Annales Henri Poincare. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01044-1. ieee: K. Kirkpatrick, S. A. E. Rademacher, and B. Schlein, “A large deviation principle in many-body quantum dynamics,” Annales Henri Poincare, vol. 22. Springer Nature, pp. 2595–2618, 2021. ista: Kirkpatrick K, Rademacher SAE, Schlein B. 2021. A large deviation principle in many-body quantum dynamics. Annales Henri Poincare. 22, 2595–2618. mla: Kirkpatrick, Kay, et al. “A Large Deviation Principle in Many-Body Quantum Dynamics.” Annales Henri Poincare, vol. 22, Springer Nature, 2021, pp. 2595–618, doi:10.1007/s00023-021-01044-1. short: K. Kirkpatrick, S.A.E. Rademacher, B. Schlein, Annales Henri Poincare 22 (2021) 2595–2618. date_created: 2021-04-25T22:01:30Z date_published: 2021-04-08T00:00:00Z date_updated: 2023-08-08T13:14:40Z day: '08' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00023-021-01044-1 ec_funded: 1 external_id: arxiv: - '2010.13754' isi: - '000638022600001' file: - access_level: open_access checksum: 1a0fb963f2f415ba470881a794f20eb6 content_type: application/pdf creator: cchlebak date_created: 2021-10-15T11:15:40Z date_updated: 2021-10-15T11:15:40Z file_id: '10143' file_name: 2021_Annales_Kirkpatrick.pdf file_size: 522669 relation: main_file success: 1 file_date_updated: 2021-10-15T11:15:40Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 2595-2618 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A large deviation principle in many-body quantum dynamics tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2021' ... --- _id: '9348' abstract: - lang: eng text: We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension. acknowledgement: GDG gratefully acknowledges the financial support of HIM Bonn in the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness, PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La Sapienza during his frequent visits. article_number: '109029' article_processing_charge: No article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Giacomo full_name: Di Gesù, Giacomo last_name: Di Gesù citation: ama: Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 2021;281(3). doi:10.1016/j.jfa.2021.109029 apa: Brooks, M., & Di Gesù, G. (2021). Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109029 chicago: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109029. ieee: M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model in infinite dimension,” Journal of Functional Analysis, vol. 281, no. 3. Elsevier, 2021. ista: Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 281(3), 109029. mla: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” Journal of Functional Analysis, vol. 281, no. 3, 109029, Elsevier, 2021, doi:10.1016/j.jfa.2021.109029. short: M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021). date_created: 2021-04-25T22:01:29Z date_published: 2021-04-07T00:00:00Z date_updated: 2023-08-08T13:15:11Z day: '07' department: - _id: RoSe doi: 10.1016/j.jfa.2021.109029 external_id: arxiv: - '1911.03187' isi: - '000644702800005' intvolume: ' 281' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1911.03187 month: '04' oa: 1 oa_version: Preprint publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Sharp tunneling estimates for a double-well model in infinite dimension type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 281 year: '2021' ... --- _id: '9462' abstract: - lang: eng text: We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions. acknowledgement: Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851. article_number: '109096' article_processing_charge: No article_type: original author: - first_name: Andreas full_name: Deuchert, Andreas last_name: Deuchert - 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, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 2021;281(6). doi:10.1016/j.jfa.2021.109096 apa: Deuchert, A., & Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109096 chicago: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109096. ieee: A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons,” Journal of Functional Analysis, vol. 281, no. 6. Elsevier, 2021. ista: Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096. mla: Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis, vol. 281, no. 6, 109096, Elsevier, 2021, doi:10.1016/j.jfa.2021.109096. short: A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021). date_created: 2021-06-06T22:01:28Z date_published: 2021-09-15T00:00:00Z date_updated: 2023-08-08T13:56:27Z day: '15' department: - _id: RoSe doi: 10.1016/j.jfa.2021.109096 ec_funded: 1 external_id: arxiv: - '2009.00992' isi: - '000656508600008' intvolume: ' 281' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2009.00992 month: '09' 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: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 281 year: '2021' ... --- _id: '9891' abstract: - lang: eng text: 'Extending on ideas of Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)], we present a modified “floating crystal” trial state for jellium (also known as the classical homogeneous electron gas) with density equal to a characteristic function. This allows us to show that three definitions of the jellium energy coincide in dimensions d ≥ 2, thus extending the result of Cotar and Petrache [“Equality of the Jellium and uniform electron gas next-order asymptotic terms for Coulomb and Riesz potentials,” arXiv: 1707.07664 (2019)] and Lewin, Lieb, and Seiringer [Phys. Rev. B 100, 035127 (2019)] that the three definitions coincide in dimension d ≥ 3. We show that the jellium energy is also equivalent to a “renormalized energy” studied in a series of papers by Serfaty and others, and thus, by the work of Bétermin and Sandier [Constr. Approximation 47, 39–74 (2018)], we relate the jellium energy to the order n term in the logarithmic energy of n points on the unit 2-sphere. We improve upon known lower bounds for this renormalized energy. Additionally, we derive formulas for the jellium energy of periodic configurations.' acknowledgement: The author would like to thank Robert Seiringer for guidance and many helpful comments on this project. The author would also like to thank Mathieu Lewin for his comments on the manuscript and Lorenzo Portinale for providing his lecture notes for the course “Mathematics of quantum many-body systems” in spring 2020, taught by Robert Seiringer. The Proof of Theorem III.1 is inspired by these lecture notes. article_number: '083305' article_processing_charge: No article_type: original author: - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: ama: Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494 apa: Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0053494 chicago: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics. AIP Publishing, 2021. https://doi.org/10.1063/5.0053494. ieee: A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” Journal of Mathematical Physics, vol. 62, no. 8. AIP Publishing, 2021. ista: Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305. mla: Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:10.1063/5.0053494. short: A.B. Lauritsen, Journal of Mathematical Physics 62 (2021). date_created: 2021-08-12T07:08:36Z date_published: 2021-08-01T00:00:00Z date_updated: 2023-08-11T10:29:48Z day: '01' ddc: - '530' department: - _id: GradSch - _id: RoSe doi: 10.1063/5.0053494 external_id: arxiv: - '2103.07975' isi: - '000683960800003' file: - access_level: open_access checksum: d035be2b894c4d50d90ac5ce252e27cd content_type: application/pdf creator: cziletti date_created: 2021-10-27T12:57:06Z date_updated: 2021-10-27T12:57:06Z file_id: '10188' file_name: 2021_JMathPhy_Lauritsen.pdf file_size: 4352640 relation: main_file success: 1 file_date_updated: 2021-10-27T12:57:06Z has_accepted_license: '1' intvolume: ' 62' isi: 1 issue: '8' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '08' oa: 1 oa_version: Published Version publication: Journal of Mathematical Physics publication_identifier: eissn: - 1089-7658 issn: - 0022-2488 publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: Floating Wigner crystal and periodic jellium configurations 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: 62 year: '2021' ... --- _id: '10224' abstract: - lang: eng text: We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging. acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. We would also like to thank Rupert Frank for many helpful discussions, especially related to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 2021;242(3):1835–1906. doi:10.1007/s00205-021-01715-7' apa: 'Feliciangeli, D., & Seiringer, R. (2021). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01715-7' chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01715-7.' ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” Archive for Rational Mechanics and Analysis, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.' ista: 'Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 242(3), 1835–1906.' mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational Mechanics and Analysis, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906, doi:10.1007/s00205-021-01715-7.' short: D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906. date_created: 2021-11-07T23:01:26Z date_published: 2021-10-25T00:00:00Z date_updated: 2023-08-14T10:32:19Z day: '25' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00205-021-01715-7 ec_funded: 1 external_id: arxiv: - '2101.12566' isi: - '000710850600001' file: - access_level: open_access checksum: 672e9c21b20f1a50854b7c821edbb92f content_type: application/pdf creator: alisjak date_created: 2021-12-14T08:35:42Z date_updated: 2021-12-14T08:35:42Z file_id: '10544' file_name: 2021_Springer_Feliciangeli.pdf file_size: 990529 relation: main_file success: 1 file_date_updated: 2021-12-14T08:35:42Z has_accepted_license: '1' intvolume: ' 242' isi: 1 issue: '3' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1835–1906 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Archive for Rational Mechanics and Analysis publication_identifier: eissn: - 1432-0673 issn: - 0003-9527 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '9787' relation: earlier_version status: public scopus_import: '1' status: public title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics' 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: 242 year: '2021' ... --- _id: '10537' abstract: - lang: eng text: We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle–hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many-body evolution can be approximated in Fock space norm by a quasi-free bosonic evolution of the collective particle–hole excitations. acknowledgement: NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM). RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates,” and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through the ERC-AdG CLaQS (Grant Agreement No. 834782). article_processing_charge: No article_type: original 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: Phan Thành full_name: Nam, Phan Thành last_name: Nam - first_name: Marcello full_name: Porta, Marcello last_name: Porta - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. 2021. doi:10.1007/s00023-021-01136-y apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2021). Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-021-01136-y chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” Annales Henri Poincaré. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01136-y. ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization of fermionic many-body dynamics,” Annales Henri Poincaré. Springer Nature, 2021. ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. mla: Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.” Annales Henri Poincaré, Springer Nature, 2021, doi:10.1007/s00023-021-01136-y. short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri Poincaré (2021). date_created: 2021-12-12T23:01:28Z date_published: 2021-12-02T00:00:00Z date_updated: 2023-08-17T06:19:14Z day: '02' department: - _id: RoSe doi: 10.1007/s00023-021-01136-y ec_funded: 1 external_id: arxiv: - '2103.08224' isi: - '000725405700001' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.08224 month: '12' 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: Annales Henri Poincaré publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Bosonization of fermionic many-body dynamics type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 year: '2021' ... --- _id: '7901' abstract: - lang: eng text: We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy. acknowledgement: We thank Christian Hainzl for helpful discussions and a referee for very careful reading of the paper and many helpful suggestions. NB and RS were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694227). Part of the research of NB was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and Peter Otte for explanations about the Luttinger model. PTN has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901). BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz Association). NB, PTN, BS, and RS acknowledge support for workshop participation from Fondation des Treilles. article_processing_charge: Yes (via OA deal) article_type: original 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: Phan Thành full_name: Nam, Phan Thành last_name: Nam - first_name: Marcello full_name: Porta, Marcello last_name: Porta - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 2021;225:885-979. doi:10.1007/s00222-021-01041-5 apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2021). Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-021-01041-5 chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.” Inventiones Mathematicae. Springer, 2021. https://doi.org/10.1007/s00222-021-01041-5. ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas,” Inventiones Mathematicae, vol. 225. Springer, pp. 885–979, 2021. ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979. mla: Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas.” Inventiones Mathematicae, vol. 225, Springer, 2021, pp. 885–979, doi:10.1007/s00222-021-01041-5. short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones Mathematicae 225 (2021) 885–979. date_created: 2020-05-28T16:48:20Z date_published: 2021-05-03T00:00:00Z date_updated: 2023-08-21T06:30:30Z day: '03' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00222-021-01041-5 ec_funded: 1 external_id: arxiv: - '2005.08933' isi: - '000646573600001' file: - access_level: open_access checksum: f38c79dfd828cdc7f49a34b37b83d376 content_type: application/pdf creator: dernst date_created: 2022-05-16T12:23:40Z date_updated: 2022-05-16T12:23:40Z file_id: '11386' file_name: 2021_InventMath_Benedikter.pdf file_size: 1089319 relation: main_file success: 1 file_date_updated: 2022-05-16T12:23:40Z has_accepted_license: '1' intvolume: ' 225' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 885-979 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Inventiones Mathematicae publication_identifier: eissn: - 1432-1297 issn: - 0020-9910 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Correlation energy of a weakly interacting 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: 225 year: '2021' ... --- _id: '7900' abstract: - lang: eng text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic systems. However, it suffers from some defects in predicting physical properties, making necessary a theory of quantum correlations. Recently, bosonization of many-body correlations has been rigorously justified as an upper bound on the correlation energy at high density with weak interactions. We review the bosonic approximation, deriving an effective Hamiltonian. We then show that for systems with Coulomb interaction this effective theory predicts collective excitations (plasmons) in accordance with the random phase approximation of Bohm and Pines, and with experimental observation. article_number: '2060009' article_processing_charge: No article_type: original author: - first_name: Niels P full_name: Benedikter, Niels P id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87 last_name: Benedikter orcid: 0000-0002-1071-6091 citation: ama: Benedikter NP. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 2021;33(1). doi:10.1142/s0129055x20600090 apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. World Scientific. https://doi.org/10.1142/s0129055x20600090 chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews in Mathematical Physics. World Scientific, 2021. https://doi.org/10.1142/s0129055x20600090. ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” Reviews in Mathematical Physics, vol. 33, no. 1. World Scientific, 2021. ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews in Mathematical Physics. 33(1), 2060009. mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” Reviews in Mathematical Physics, vol. 33, no. 1, 2060009, World Scientific, 2021, doi:10.1142/s0129055x20600090. short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021). date_created: 2020-05-28T16:47:55Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-09-05T16:07:40Z day: '01' department: - _id: RoSe doi: 10.1142/s0129055x20600090 ec_funded: 1 external_id: arxiv: - '1910.08190' isi: - '000613313200010' intvolume: ' 33' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.08190 month: '01' 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: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific quality_controlled: '1' scopus_import: '1' status: public title: Bosonic collective excitations in Fermi gases type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 33 year: '2021' ... --- _id: '10852' abstract: - lang: eng text: ' We review old and new results on the Fröhlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.' acknowledgement: This work was supported by the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo. 694227). article_number: '2060012' article_processing_charge: No article_type: original author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Seiringer R. The polaron at strong coupling. Reviews in Mathematical Physics. 2021;33(01). doi:10.1142/s0129055x20600120 apa: Seiringer, R. (2021). The polaron at strong coupling. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x20600120 chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics. World Scientific Publishing, 2021. https://doi.org/10.1142/s0129055x20600120. ieee: R. Seiringer, “The polaron at strong coupling,” Reviews in Mathematical Physics, vol. 33, no. 01. World Scientific Publishing, 2021. ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical Physics. 33(01), 2060012. mla: Seiringer, Robert. “The Polaron at Strong Coupling.” Reviews in Mathematical Physics, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:10.1142/s0129055x20600120. short: R. Seiringer, Reviews in Mathematical Physics 33 (2021). date_created: 2022-03-18T08:11:34Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-05T16:08:02Z day: '01' department: - _id: RoSe doi: 10.1142/s0129055x20600120 ec_funded: 1 external_id: arxiv: - '1912.12509' isi: - '000613313200013' intvolume: ' 33' isi: 1 issue: '01' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.12509 month: '02' 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: Reviews in Mathematical Physics publication_identifier: eissn: - 1793-6659 issn: - 0129-055X publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: The polaron at strong coupling type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 33 year: '2021' ... --- _id: '9225' abstract: - lang: eng text: "The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.\r\nHere, we provide a class of initial data for which the associated effective Hamiltonian\r\nhas a uniform spectral gap for all times. For such initial data, this allows us to extend the\r\nresults on the adiabatic theorem for the Landau–Pekar equations and their derivation\r\nfrom the Fröhlich model obtained in previous works to larger times." acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No 694227 (D.F. and R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged. Open Access funding provided by Institute of Science and Technology (IST Austria) article_number: '19' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Feliciangeli D, Rademacher SAE, Seiringer R. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 2021;111. doi:10.1007/s11005-020-01350-5 apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2021). Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01350-5 chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s11005-020-01350-5. ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “Persistence of the spectral gap for the Landau–Pekar equations,” Letters in Mathematical Physics, vol. 111. Springer Nature, 2021. ista: Feliciangeli D, Rademacher SAE, Seiringer R. 2021. Persistence of the spectral gap for the Landau–Pekar equations. Letters in Mathematical Physics. 111, 19. mla: Feliciangeli, Dario, et al. “Persistence of the Spectral Gap for the Landau–Pekar Equations.” Letters in Mathematical Physics, vol. 111, 19, Springer Nature, 2021, doi:10.1007/s11005-020-01350-5. short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Letters in Mathematical Physics 111 (2021). date_created: 2021-03-07T23:01:25Z date_published: 2021-02-11T00:00:00Z date_updated: 2023-09-07T13:30:11Z day: '11' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-020-01350-5 ec_funded: 1 external_id: isi: - '000617195700001' file: - access_level: open_access checksum: ffbfe1aad623bce7ff529c207e343b53 content_type: application/pdf creator: dernst date_created: 2021-03-09T11:44:34Z date_updated: 2021-03-09T11:44:34Z file_id: '9232' file_name: 2021_LettersMathPhysics_Feliciangeli.pdf file_size: 391205 relation: main_file success: 1 file_date_updated: 2021-03-09T11:44:34Z has_accepted_license: '1' intvolume: ' 111' isi: 1 language: - iso: eng month: '02' 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: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Letters in Mathematical Physics publication_identifier: eissn: - '15730530' issn: - '03779017' publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '9733' relation: dissertation_contains status: public scopus_import: '1' status: public title: Persistence of the spectral gap for the Landau–Pekar 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 111 year: '2021' ... --- _id: '9787' abstract: - lang: eng text: We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging. acknowledgement: "Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. We would also like to thank Rupert Frank for many helpful discussions, especially related to the Gross coordinate transformation defined in Def. 4.1.\r\n" article_number: '2101.12566' article_processing_charge: No author: - first_name: Dario full_name: Feliciangeli, Dario id: 41A639AA-F248-11E8-B48F-1D18A9856A87 last_name: Feliciangeli orcid: 0000-0003-0754-8530 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv.' apa: 'Feliciangeli, D., & Seiringer, R. (n.d.). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv.' chicago: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, n.d.' ieee: 'D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” arXiv. .' ista: 'Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. arXiv, 2101.12566.' mla: 'Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” ArXiv, 2101.12566.' short: D. Feliciangeli, R. Seiringer, ArXiv (n.d.). date_created: 2021-08-06T08:25:57Z date_published: 2021-02-01T00:00:00Z date_updated: 2023-09-07T13:30:10Z day: '01' ddc: - '510' department: - _id: RoSe ec_funded: 1 external_id: arxiv: - '2101.12566' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2101.12566 month: '02' 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: arXiv publication_status: submitted related_material: record: - id: '10224' relation: later_version status: public - id: '9733' relation: dissertation_contains status: public status: public title: 'The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics' 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: preprint user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 year: '2021' ... --- _id: '10738' abstract: - lang: eng text: We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2. acknowledgement: "N. L. and R. S. gratefully acknowledge financial support by the European Research Council\r\n(ERC) under the European Union’s Horizon 2020 research and innovation programme (grant\r\nagreement No 694227). B. S. acknowledges support from the Swiss National Science Foundation (grant 200020_172623) and from the NCCR SwissMAP. N. L. would like to thank\r\nAndreas Deuchert and David Mitrouskas for interesting discussions. B. S. and R. S. would\r\nlike to thank Rupert Frank for stimulating discussions about the time-evolution of a polaron.\r\n" article_processing_charge: No 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: Simone Anna Elvira full_name: Rademacher, Simone Anna Elvira id: 856966FE-A408-11E9-977E-802DE6697425 last_name: Rademacher orcid: 0000-0001-5059-4466 - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 2021;14(7):2079-2100. doi:10.2140/APDE.2021.14.2079' apa: 'Leopold, N. K., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. Mathematical Sciences Publishers. https://doi.org/10.2140/APDE.2021.14.2079' chicago: 'Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/APDE.2021.14.2079.' ieee: 'N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “ The Landau–Pekar equations: Adiabatic theorem and accuracy,” Analysis and PDE, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.' ista: 'Leopold NK, Rademacher SAE, Schlein B, Seiringer R. 2021. The Landau–Pekar equations: Adiabatic theorem and accuracy. Analysis and PDE. 14(7), 2079–2100.' mla: 'Leopold, Nikolai K., et al. “ The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” Analysis and PDE, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:10.2140/APDE.2021.14.2079.' short: N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100. date_created: 2022-02-06T23:01:33Z date_published: 2021-11-10T00:00:00Z date_updated: 2023-10-17T11:26:45Z day: '10' department: - _id: RoSe doi: 10.2140/APDE.2021.14.2079 ec_funded: 1 external_id: arxiv: - '1904.12532' isi: - '000733976600004' intvolume: ' 14' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1904.12532 month: '11' oa: 1 oa_version: Preprint page: 2079-2100 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Analysis and PDE publication_identifier: eissn: - 1948-206X issn: - 2157-5045 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: ' The Landau–Pekar equations: Adiabatic theorem and accuracy' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 14 year: '2021' ...