--- _id: '9792' 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 careful 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 thanks 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. Finally, the authors also thanks J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and NoF65. D.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 European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].' article_number: '2106.11217' 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: 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. arXiv. doi:10.48550/arXiv.2106.11217 apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv. https://doi.org/10.48550/arXiv.2106.11217 chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2106.11217. ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” arXiv. . ista: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217. mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” ArXiv, 2106.11217, doi:10.48550/arXiv.2106.11217. short: D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.). date_created: 2021-08-06T09:07:12Z date_published: 2021-07-21T00:00:00Z date_updated: 2023-11-14T13:21:01Z day: '21' ddc: - '510' department: - _id: RoSe - _id: JaMa doi: 10.48550/arXiv.2106.11217 ec_funded: 1 external_id: arxiv: - '2106.11217' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2106.11217 month: '07' oa: 1 oa_version: Preprint project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication: arXiv publication_status: submitted related_material: record: - id: '9733' relation: dissertation_contains status: public - id: '10030' relation: dissertation_contains status: public - id: '12911' relation: later_version status: public status: public title: A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '14889' abstract: - lang: eng text: We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2. acknowledgement: "Financial support by the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie grant agreement No. 754411 (S.R.) and the European\r\nResearch Council under grant agreement No. 694227 (N.L. and R.S.), as well as by the SNSF\r\nEccellenza project PCEFP2 181153 (N.L.), the NCCR SwissMAP (N.L. and B.S.) and by the\r\nDeutsche Forschungsgemeinschaft (DFG) through the Research Training Group 1838: Spectral\r\nTheory and Dynamics of Quantum Systems (D.M.) is gratefully acknowledged. B.S. gratefully\r\nacknowledges financial support from the Swiss National Science Foundation through the Grant\r\n“Dynamical and energetic properties of Bose-Einstein condensates” and from the European\r\nResearch Council through the ERC-AdG CLaQS (grant agreement No 834782). D.M. thanks\r\nMarcel Griesemer for helpful discussions." 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: 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, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 2021;3(4):653-676. doi:10.2140/paa.2021.3.653 apa: Leopold, N. K., Mitrouskas, D. J., Rademacher, S. A. E., Schlein, B., & Seiringer, R. (2021). Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2021.3.653 chicago: Leopold, Nikolai K, David Johannes Mitrouskas, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.653. ieee: N. K. Leopold, D. J. Mitrouskas, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 653–676, 2021. ista: Leopold NK, Mitrouskas DJ, Rademacher SAE, Schlein B, Seiringer R. 2021. Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron. Pure and Applied Analysis. 3(4), 653–676. mla: Leopold, Nikolai K., et al. “Landau–Pekar Equations and Quantum Fluctuations for the Dynamics of a Strongly Coupled Polaron.” Pure and Applied Analysis, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 653–76, doi:10.2140/paa.2021.3.653. short: N.K. Leopold, D.J. Mitrouskas, S.A.E. Rademacher, B. Schlein, R. Seiringer, Pure and Applied Analysis 3 (2021) 653–676. date_created: 2024-01-28T23:01:43Z date_published: 2021-10-01T00:00:00Z date_updated: 2024-02-05T10:02:45Z day: '01' department: - _id: RoSe doi: 10.2140/paa.2021.3.653 ec_funded: 1 external_id: arxiv: - '2005.02098' intvolume: ' 3' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2005.02098 month: '10' oa: 1 oa_version: Preprint page: 653-676 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: Pure and Applied Analysis publication_identifier: eissn: - 2578-5885 issn: - 2578-5893 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2021' ... --- _id: '14890' abstract: - lang: eng text: We consider a system of N interacting bosons in the mean-field scaling regime and construct corrections to the Bogoliubov dynamics that approximate the true N-body dynamics in norm to arbitrary precision. The N-independent corrections are given in terms of the solutions of the Bogoliubov and Hartree equations and satisfy a generalized form of Wick's theorem. We determine the n-point correlation functions of the excitations around the condensate, as well as the reduced densities of the N-body system, to arbitrary accuracy, given only the knowledge of the two-point functions of a quasi-free state and the solution of the Hartree equation. In this way, the complex problem of computing all n-point correlation functions for an interacting N-body system is essentially reduced to the problem of solving the Hartree equation and the PDEs for the Bogoliubov two-point functions. acknowledgement: "We are grateful for the hospitality of Central China Normal University (CCNU),\r\nwhere parts of this work were done, and thank Phan Th`anh Nam, Simone\r\nRademacher, Robert Seiringer and Stefan Teufel for helpful discussions. L.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research\r\nTraining Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and the funding\r\nfrom the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSk lodowska-Curie Grant Agreement No. 754411." article_processing_charge: No 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: Peter full_name: Pickl, Peter last_name: Pickl - first_name: Avy full_name: Soffer, Avy last_name: Soffer citation: ama: Bossmann L, Petrat SP, Pickl P, Soffer A. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 2021;3(4):677-726. doi:10.2140/paa.2021.3.677 apa: Bossmann, L., Petrat, S. P., Pickl, P., & Soffer, A. (2021). Beyond Bogoliubov dynamics. Pure and Applied Analysis. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2021.3.677 chicago: Bossmann, Lea, Sören P Petrat, Peter Pickl, and Avy Soffer. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/paa.2021.3.677. ieee: L. Bossmann, S. P. Petrat, P. Pickl, and A. Soffer, “Beyond Bogoliubov dynamics,” Pure and Applied Analysis, vol. 3, no. 4. Mathematical Sciences Publishers, pp. 677–726, 2021. ista: Bossmann L, Petrat SP, Pickl P, Soffer A. 2021. Beyond Bogoliubov dynamics. Pure and Applied Analysis. 3(4), 677–726. mla: Bossmann, Lea, et al. “Beyond Bogoliubov Dynamics.” Pure and Applied Analysis, vol. 3, no. 4, Mathematical Sciences Publishers, 2021, pp. 677–726, doi:10.2140/paa.2021.3.677. short: L. Bossmann, S.P. Petrat, P. Pickl, A. Soffer, Pure and Applied Analysis 3 (2021) 677–726. date_created: 2024-01-28T23:01:43Z date_published: 2021-10-01T00:00:00Z date_updated: 2024-02-05T09:26:31Z day: '01' department: - _id: RoSe doi: 10.2140/paa.2021.3.677 ec_funded: 1 external_id: arxiv: - '1912.11004' intvolume: ' 3' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1912.11004 month: '10' oa: 1 oa_version: Preprint page: 677-726 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Pure and Applied Analysis publication_identifier: eissn: - 2578-5885 issn: - 2578-5893 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Beyond Bogoliubov dynamics type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 3 year: '2021' ... --- _id: '9733' abstract: - lang: eng text: This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author. alternative_title: - ISTA Thesis 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 citation: ama: Feliciangeli D. The polaron at strong coupling. 2021. doi:10.15479/at:ista:9733 apa: Feliciangeli, D. (2021). The polaron at strong coupling. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:9733 chicago: Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:9733. ieee: D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021. ista: Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria. mla: Feliciangeli, Dario. The Polaron at Strong Coupling. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:9733. short: D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021. date_created: 2021-07-27T15:48:30Z date_published: 2021-08-20T00:00:00Z date_updated: 2024-03-06T12:30:44Z day: '20' ddc: - '515' - '519' - '539' degree_awarded: PhD department: - _id: GradSch - _id: RoSe - _id: JaMa doi: 10.15479/at:ista:9733 ec_funded: 1 file: - access_level: open_access checksum: e88bb8ca43948abe060eb2d2fa719881 content_type: application/pdf creator: dfelicia date_created: 2021-08-19T14:03:48Z date_updated: 2021-09-06T09:28:56Z file_id: '9944' file_name: Thesis_FeliciangeliA.pdf file_size: 1958710 relation: main_file - access_level: closed checksum: 72810843abee83705853505b3f8348aa content_type: application/octet-stream creator: dfelicia date_created: 2021-08-19T14:06:35Z date_updated: 2022-03-10T12:13:57Z file_id: '9945' file_name: thesis.7z file_size: 3771669 relation: source_file file_date_updated: 2022-03-10T12:13:57Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '08' oa: 1 oa_version: Published Version page: '180' 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: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9787' relation: part_of_dissertation status: public - id: '9792' relation: part_of_dissertation status: public - id: '9225' relation: part_of_dissertation status: public - id: '9781' relation: part_of_dissertation status: public - id: '9791' 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 - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 title: The polaron at strong coupling tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2021' ... --- _id: '9791' abstract: - lang: eng text: We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar 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 Landau and Pekar. acknowledgement: We thank Herbert Spohn for helpful comments. 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.. article_number: '2107.03720 ' 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: 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. arXiv. apa: Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (n.d.). The effective mass problem for the Landau-Pekar equations. arXiv. chicago: Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, n.d. ieee: D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” arXiv. . ista: Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. arXiv, 2107.03720. mla: Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” ArXiv, 2107.03720. short: D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, ArXiv (n.d.). date_created: 2021-08-06T08:49:45Z date_published: 2021-07-08T00:00:00Z date_updated: 2024-03-06T12:30:45Z day: '08' ddc: - '510' department: - _id: RoSe ec_funded: 1 external_id: arxiv: - '2107.03720' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2107.03720 month: '07' oa: 1 oa_version: Preprint 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: arXiv publication_status: submitted related_material: record: - id: '10755' relation: later_version status: public - id: '9733' relation: dissertation_contains status: public status: public title: The effective mass problem for the Landau-Pekar equations type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '6649' abstract: - lang: eng text: "While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n" 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. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 2020;374:2097–2150. doi:10.1007/s00220-019-03505-5 apa: Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03505-5 chicago: Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03505-5. ieee: N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” Communications in Mathematical Physics, vol. 374. Springer Nature, pp. 2097–2150, 2020. ista: Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150. mla: Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” Communications in Mathematical Physics, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:10.1007/s00220-019-03505-5. short: N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150. date_created: 2019-07-18T13:30:04Z date_published: 2020-03-01T00:00:00Z date_updated: 2023-08-17T13:51:50Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00220-019-03505-5 ec_funded: 1 external_id: arxiv: - '1809.01902' isi: - '000527910700019' file: - access_level: open_access checksum: f9dd6dd615a698f1d3636c4a092fed23 content_type: application/pdf creator: dernst date_created: 2019-07-24T07:19:10Z date_updated: 2020-07-14T12:47:35Z file_id: '6668' file_name: 2019_CommMathPhysics_Benedikter.pdf file_size: 853289 relation: main_file file_date_updated: 2020-07-14T12:47:35Z has_accepted_license: '1' intvolume: ' 374' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 2097–2150 project: - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems - _id: 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: Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime 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: 374 year: '2020' ... --- _id: '7508' abstract: - lang: eng text: In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider the dynamics of N d-dimensional bosons for large N. The bosons initially form a Bose–Einstein condensate and interact with each other via a pair potential of the form (N−1)−1Ndβv(Nβ·)forβ∈[0,14d). We derive a sequence of N-body functions which approximate the true many-body dynamics in L2(RdN)-norm to arbitrary precision in powers of N−1. The approximating functions are constructed as Duhamel expansions of finite order in terms of the first quantised analogue of a Bogoliubov time evolution. acknowledgement: "Open access funding provided by Institute of Science and Technology (IST Austria).\r\nL.B. gratefully acknowledges the support by the German Research Foundation (DFG) within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems”, and wishes to thank Stefan Teufel, Sören Petrat and Marcello Porta for helpful discussions. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. N.P. gratefully acknowledges support from NSF grant DMS-1516228 and DMS-1840314. P.P.’s research was funded by DFG Grant no. PI 1114/3-1. Part of this work was done when N.P. and P.P. were visiting CCNU, Wuhan. N.P. and P.P. thank A.S. for his hospitality at CCNU." 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: Nataša full_name: Pavlović, Nataša last_name: Pavlović - first_name: Peter full_name: Pickl, Peter last_name: Pickl - first_name: Avy full_name: Soffer, Avy last_name: Soffer citation: ama: Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. 2020;178:1362-1396. doi:10.1007/s10955-020-02500-8 apa: Bossmann, L., Pavlović, N., Pickl, P., & Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-020-02500-8 chicago: Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02500-8. ieee: L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” Journal of Statistical Physics, vol. 178. Springer Nature, pp. 1362–1396, 2020. ista: Bossmann L, Pavlović N, Pickl P, Soffer A. 2020. Higher order corrections to the mean-field description of the dynamics of interacting bosons. Journal of Statistical Physics. 178, 1362–1396. mla: Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” Journal of Statistical Physics, vol. 178, Springer Nature, 2020, pp. 1362–96, doi:10.1007/s10955-020-02500-8. short: L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics 178 (2020) 1362–1396. date_created: 2020-02-23T09:45:51Z date_published: 2020-02-21T00:00:00Z date_updated: 2023-08-18T06:37:46Z day: '21' ddc: - '510' department: - _id: RoSe doi: 10.1007/s10955-020-02500-8 ec_funded: 1 external_id: arxiv: - '1905.06164' isi: - '000516342200001' file: - access_level: open_access checksum: 643e230bf147e64d9cdb3f6cc573679d content_type: application/pdf creator: dernst date_created: 2020-11-20T09:26:46Z date_updated: 2020-11-20T09:26:46Z file_id: '8780' file_name: 2020_JournStatPhysics_Bossmann.pdf file_size: 576726 relation: main_file success: 1 file_date_updated: 2020-11-20T09:26:46Z has_accepted_license: '1' intvolume: ' 178' isi: 1 language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 1362-1396 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _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: Higher order corrections to the mean-field description of the dynamics of 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: 178 year: '2020' ... --- _id: '7790' abstract: - lang: eng text: "We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density \U0001D70C and inverse temperature \U0001D6FD differs from the one of the noninteracting system by the correction term \U0001D70B\U0001D70C\U0001D70C\U0001D6FD\U0001D6FD . Here, is the scattering length of the interaction potential, and \U0001D6FD is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit \U0001D70C and if \U0001D6FD\U0001D70C ." article_number: e20 article_processing_charge: No article_type: original author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.17 apa: Deuchert, A., Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2020.17 chicago: Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics, Sigma. Cambridge University Press, 2020. https://doi.org/10.1017/fms.2020.17. ieee: A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” Forum of Mathematics, Sigma, vol. 8. Cambridge University Press, 2020. ista: Deuchert A, Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. Forum of Mathematics, Sigma. 8, e20. mla: Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” Forum of Mathematics, Sigma, vol. 8, e20, Cambridge University Press, 2020, doi:10.1017/fms.2020.17. short: A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020). date_created: 2020-05-03T22:00:48Z date_published: 2020-03-14T00:00:00Z date_updated: 2023-08-21T06:18:49Z day: '14' ddc: - '510' department: - _id: RoSe doi: 10.1017/fms.2020.17 ec_funded: 1 external_id: arxiv: - '1910.03372' isi: - '000527342000001' file: - access_level: open_access checksum: 8a64da99d107686997876d7cad8cfe1e content_type: application/pdf creator: dernst date_created: 2020-05-04T12:02:41Z date_updated: 2020-07-14T12:48:03Z file_id: '7797' file_name: 2020_ForumMath_Deuchert.pdf file_size: 692530 relation: main_file file_date_updated: 2020-07-14T12:48:03Z has_accepted_license: '1' intvolume: ' 8' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' related_material: record: - id: '7524' relation: earlier_version status: public scopus_import: '1' status: public title: The free energy of the two-dimensional dilute Bose gas. I. Lower bound 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: 8 year: '2020' ... --- _id: '8042' abstract: - lang: eng text: We consider systems of N bosons in a box of volume one, interacting through a repulsive two-body potential of the form κN3β−1V(Nβx). For all 0<β<1, and for sufficiently small coupling constant κ>0, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large N. article_processing_charge: No article_type: original author: - first_name: Chiara full_name: Boccato, Chiara id: 342E7E22-F248-11E8-B48F-1D18A9856A87 last_name: Boccato - first_name: Christian full_name: Brennecke, Christian last_name: Brennecke - first_name: Serena full_name: Cenatiempo, Serena last_name: Cenatiempo - first_name: Benjamin full_name: Schlein, Benjamin last_name: Schlein citation: ama: Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of Bose gases interacting through singular potentials. Journal of the European Mathematical Society. 2020;22(7):2331-2403. doi:10.4171/JEMS/966 apa: Boccato, C., Brennecke, C., Cenatiempo, S., & Schlein, B. (2020). The excitation spectrum of Bose gases interacting through singular potentials. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/966 chicago: Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” Journal of the European Mathematical Society. European Mathematical Society, 2020. https://doi.org/10.4171/JEMS/966. ieee: C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum of Bose gases interacting through singular potentials,” Journal of the European Mathematical Society, vol. 22, no. 7. European Mathematical Society, pp. 2331–2403, 2020. ista: Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. The excitation spectrum of Bose gases interacting through singular potentials. Journal of the European Mathematical Society. 22(7), 2331–2403. mla: Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” Journal of the European Mathematical Society, vol. 22, no. 7, European Mathematical Society, 2020, pp. 2331–403, doi:10.4171/JEMS/966. short: C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European Mathematical Society 22 (2020) 2331–2403. date_created: 2020-06-29T07:59:35Z date_published: 2020-07-01T00:00:00Z date_updated: 2023-08-22T07:47:04Z day: '01' department: - _id: RoSe doi: 10.4171/JEMS/966 external_id: arxiv: - '1704.04819' isi: - '000548174700006' intvolume: ' 22' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1704.04819 month: '07' oa: 1 oa_version: Preprint page: 2331-2403 publication: Journal of the European Mathematical Society publication_identifier: issn: - '14359855' publication_status: published publisher: European Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: The excitation spectrum of Bose gases interacting through singular potentials type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2020' ... --- _id: '8091' abstract: - lang: eng text: In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level. acknowledgement: "Open access funding provided by Institute of Science and Technology (IST Austria).\r\nThe work of R.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. " 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: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 2020;181:448-464. doi:10.1007/s10955-020-02586-0 apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-020-02586-0 chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics. Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0. ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” Journal of Statistical Physics, vol. 181. Springer, pp. 448–464, 2020. ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464. mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics, vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0. short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464. date_created: 2020-07-05T22:00:46Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T07:51:47Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s10955-020-02586-0 ec_funded: 1 external_id: arxiv: - '2001.07144' isi: - '000543030000002' file: - access_level: open_access checksum: 5cbeef52caf18d0d952f17fed7b5545a content_type: application/pdf creator: dernst date_created: 2020-11-25T15:05:04Z date_updated: 2020-11-25T15:05:04Z file_id: '8812' file_name: 2020_JourStatPhysics_Seiringer.pdf file_size: 404778 relation: main_file success: 1 file_date_updated: 2020-11-25T15:05:04Z has_accepted_license: '1' intvolume: ' 181' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 448-464 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: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Emergence of Haldane pseudo-potentials in systems with short-range interactions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 181 year: '2020' ... --- _id: '8134' abstract: - lang: eng text: We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ ≪ 1 and βρ ≳ 1, the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2|lna2ρ|−1(2−[1−βc/β]2+) to leading order, where a is the scattering length of the two-body interaction potential, ρ is the density, β is the inverse temperature, and βc is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved by Deuchert et al. [Forum Math. Sigma 8, e20 (2020)], this shows equality in the asymptotic expansion. article_number: '061901' article_processing_charge: No article_type: original author: - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 2020;61(6). doi:10.1063/5.0005950 apa: Mayer, S., & Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0005950 chicago: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics. AIP Publishing, 2020. https://doi.org/10.1063/5.0005950. ieee: S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” Journal of Mathematical Physics, vol. 61, no. 6. AIP Publishing, 2020. ista: Mayer S, Seiringer R. 2020. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. Journal of Mathematical Physics. 61(6), 061901. mla: Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” Journal of Mathematical Physics, vol. 61, no. 6, 061901, AIP Publishing, 2020, doi:10.1063/5.0005950. short: S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020). date_created: 2020-07-19T22:00:59Z date_published: 2020-06-22T00:00:00Z date_updated: 2023-08-22T08:12:40Z day: '22' department: - _id: RoSe doi: 10.1063/5.0005950 ec_funded: 1 external_id: arxiv: - '2002.08281' isi: - '000544595100001' intvolume: ' 61' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.08281 month: '06' 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 Mathematical Physics publication_identifier: issn: - '00222488' publication_status: published publisher: AIP Publishing quality_controlled: '1' scopus_import: '1' status: public title: The free energy of the two-dimensional dilute Bose gas. II. Upper bound type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 61 year: '2020' ... --- _id: '8769' abstract: - lang: eng text: One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding many-particle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes or vortices to it and thereby converts it into an Abelian anyon. The corresponding quantum impurity model, first, provides a different approach to the numerical solution of the many-anyon problem, along with a concrete perspective of anyons as emergent quasiparticles built from composite bosons or fermions. More importantly, the model paves the way toward realizing anyons using impurities in crystal lattices as well as ultracold gases. In particular, we consider two heavy electrons interacting with a two-dimensional lattice crystal in a magnetic field, and show that when the impurity-bath system is rotated at the cyclotron frequency, impurities behave as anyons as a consequence of the angular momentum exchange between the impurities and the bath. A possible experimental realization is proposed by identifying the statistics parameter in terms of the mean-square distance of the impurities and the magnetization of the impurity-bath system, both of which are accessible to experiment. Another proposed application is impurities immersed in a two-dimensional weakly interacting Bose gas. acknowledgement: "We are grateful to M. Correggi, A. Deuchert, and P. Schmelcher for valuable discussions. We also thank the anonymous referees for helping to clarify a few important points in the experimental realization. A.G. acknowledges support by the European Unions Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement\r\nNo 754411. D.L. acknowledges financial support from the Goran Gustafsson Foundation (grant no. 1804) and LMU Munich. R.S., M.L., and N.R. gratefully acknowledge financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 694227, No 801770, and No 758620, respectively)." article_number: '144109' article_processing_charge: No article_type: original author: - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 - first_name: Areg full_name: Ghazaryan, Areg id: 4AF46FD6-F248-11E8-B48F-1D18A9856A87 last_name: Ghazaryan orcid: 0000-0001-9666-3543 - first_name: D. full_name: Lundholm, D. last_name: Lundholm - first_name: N. full_name: Rougerie, N. last_name: Rougerie - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R. Quantum impurity model for anyons. Physical Review B. 2020;102(14). doi:10.1103/physrevb.102.144109 apa: Yakaboylu, E., Ghazaryan, A., Lundholm, D., Rougerie, N., Lemeshko, M., & Seiringer, R. (2020). Quantum impurity model for anyons. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.102.144109 chicago: Yakaboylu, Enderalp, Areg Ghazaryan, D. Lundholm, N. Rougerie, Mikhail Lemeshko, and Robert Seiringer. “Quantum Impurity Model for Anyons.” Physical Review B. American Physical Society, 2020. https://doi.org/10.1103/physrevb.102.144109. ieee: E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, and R. Seiringer, “Quantum impurity model for anyons,” Physical Review B, vol. 102, no. 14. American Physical Society, 2020. ista: Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R. 2020. Quantum impurity model for anyons. Physical Review B. 102(14), 144109. mla: Yakaboylu, Enderalp, et al. “Quantum Impurity Model for Anyons.” Physical Review B, vol. 102, no. 14, 144109, American Physical Society, 2020, doi:10.1103/physrevb.102.144109. short: E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, R. Seiringer, Physical Review B 102 (2020). date_created: 2020-11-18T07:34:17Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-09-05T12:12:30Z day: '01' department: - _id: MiLe - _id: RoSe doi: 10.1103/physrevb.102.144109 ec_funded: 1 external_id: arxiv: - '1912.07890' isi: - '000582563300001' intvolume: ' 102' isi: 1 issue: '14' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.07890 month: '10' oa: 1 oa_version: Preprint 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 - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' publication: Physical Review B publication_identifier: eissn: - 2469-9969 issn: - 2469-9950 publication_status: published publisher: American Physical Society quality_controlled: '1' scopus_import: '1' status: public title: Quantum impurity model for anyons type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 102 year: '2020' ... --- _id: '7650' abstract: - lang: eng text: We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). It is a pleasure to thank Jakob Yngvason for helpful discussions. Financial support by the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation programme (Grant Agreement No. 694227) is gratefully acknowledged. A. D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 836146. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 2020;236(6):1217-1271. doi:10.1007/s00205-020-01489-4 apa: Deuchert, A., & Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-020-01489-4 chicago: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01489-4. ieee: A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature,” Archive for Rational Mechanics and Analysis, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020. ista: Deuchert A, Seiringer R. 2020. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. Archive for Rational Mechanics and Analysis. 236(6), 1217–1271. mla: Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” Archive for Rational Mechanics and Analysis, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:10.1007/s00205-020-01489-4. short: A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 1217–1271. date_created: 2020-04-08T15:18:03Z date_published: 2020-03-09T00:00:00Z date_updated: 2023-09-05T14:18:49Z day: '09' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00205-020-01489-4 ec_funded: 1 external_id: arxiv: - '1901.11363' isi: - '000519415000001' file: - access_level: open_access checksum: b645fb64bfe95bbc05b3eea374109a9c content_type: application/pdf creator: dernst date_created: 2020-11-20T13:17:42Z date_updated: 2020-11-20T13:17:42Z file_id: '8785' file_name: 2020_ArchRatMechanicsAnalysis_Deuchert.pdf file_size: 704633 relation: main_file success: 1 file_date_updated: 2020-11-20T13:17:42Z has_accepted_license: '1' intvolume: ' 236' isi: 1 issue: '6' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 1217-1271 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: 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: Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 236 year: '2020' ... --- _id: '8130' abstract: - lang: eng text: We study the dynamics of a system of N interacting bosons in a disc-shaped trap, which is realised by an external potential that confines the bosons in one spatial dimension to an interval of length of order ε. The interaction is non-negative and scaled in such a way that its scattering length is of order ε/N, while its range is proportional to (ε/N)β with scaling parameter β∈(0,1]. We consider the simultaneous limit (N,ε)→(∞,0) and assume that the system initially exhibits Bose–Einstein condensation. We prove that condensation is preserved by the N-body dynamics, where the time-evolved condensate wave function is the solution of a two-dimensional non-linear equation. The strength of the non-linearity depends on the scaling parameter β. For β∈(0,1), we obtain a cubic defocusing non-linear Schrödinger equation, while the choice β=1 yields a Gross–Pitaevskii equation featuring the scattering length of the interaction. In both cases, the coupling parameter depends on the confining potential. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). I thank Stefan Teufel for helpful remarks and for his involvement in the closely related joint project [10]. Helpful discussions with Serena Cenatiempo and Nikolai Leopold are gratefully acknowledged. This work was supported by the German Research Foundation within the Research Training Group 1838 “Spectral Theory and Dynamics of Quantum Systems” and has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. 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. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 2020;238(11):541-606. doi:10.1007/s00205-020-01548-w apa: Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-020-01548-w chicago: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” Archive for Rational Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-020-01548-w. ieee: L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” Archive for Rational Mechanics and Analysis, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020. ista: Bossmann L. 2020. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. Archive for Rational Mechanics and Analysis. 238(11), 541–606. mla: Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” Archive for Rational Mechanics and Analysis, vol. 238, no. 11, Springer Nature, 2020, pp. 541–606, doi:10.1007/s00205-020-01548-w. short: L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606. date_created: 2020-07-18T15:06:35Z date_published: 2020-11-01T00:00:00Z date_updated: 2023-09-05T14:19:06Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00205-020-01548-w ec_funded: 1 external_id: arxiv: - '1907.04547' isi: - '000550164400001' file: - access_level: open_access checksum: cc67a79a67bef441625fcb1cd031db3d content_type: application/pdf creator: dernst date_created: 2020-12-02T08:50:38Z date_updated: 2020-12-02T08:50:38Z file_id: '8826' file_name: 2020_ArchiveRatMech_Bossmann.pdf file_size: 942343 relation: main_file success: 1 file_date_updated: 2020-12-02T08:50:38Z has_accepted_license: '1' intvolume: ' 238' isi: 1 issue: '11' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 541-606 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: 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: Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 238 year: '2020' ... --- _id: '7235' abstract: - lang: eng text: We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). 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.) is gratefully acknowledged. article_processing_charge: Yes (via OA deal) article_type: original author: - 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: Lieb EH, Seiringer R. Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. 2020;180:23-33. doi:10.1007/s10955-019-02322-3 apa: Lieb, E. H., & Seiringer, R. (2020). Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02322-3 chicago: Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02322-3. ieee: E. H. Lieb and R. Seiringer, “Divergence of the effective mass of a polaron in the strong coupling limit,” Journal of Statistical Physics, vol. 180. Springer Nature, pp. 23–33, 2020. ista: Lieb EH, Seiringer R. 2020. Divergence of the effective mass of a polaron in the strong coupling limit. Journal of Statistical Physics. 180, 23–33. mla: Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” Journal of Statistical Physics, vol. 180, Springer Nature, 2020, pp. 23–33, doi:10.1007/s10955-019-02322-3. short: E.H. Lieb, R. Seiringer, Journal of Statistical Physics 180 (2020) 23–33. date_created: 2020-01-07T09:42:03Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-09-05T14:57:29Z day: '01' ddc: - '510' - '530' department: - _id: RoSe doi: 10.1007/s10955-019-02322-3 ec_funded: 1 external_id: isi: - '000556199700003' file: - access_level: open_access checksum: 1e67bee6728592f7bdcea2ad2d9366dc content_type: application/pdf creator: dernst date_created: 2020-11-19T11:13:55Z date_updated: 2020-11-19T11:13:55Z file_id: '8774' file_name: 2020_JourStatPhysics_Lieb.pdf file_size: 279749 relation: main_file success: 1 file_date_updated: 2020-11-19T11:13:55Z has_accepted_license: '1' intvolume: ' 180' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 23-33 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: 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: Divergence of the effective mass of a polaron 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 180 year: '2020' ... --- _id: '7611' abstract: - lang: eng text: We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem. acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP. This project has received\r\nfunding from the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R. would like to thank Benjamin Schlein for many fruitful discussions." 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 citation: ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. 2020;110:2143-2174. doi:10.1007/s11005-020-01286-w apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01286-w chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” Letters in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s11005-020-01286-w. ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through singular potentials,” Letters in Mathematical Physics, vol. 110. Springer Nature, pp. 2143–2174, 2020. ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through singular potentials. Letters in Mathematical Physics. 110, 2143–2174. mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” Letters in Mathematical Physics, vol. 110, Springer Nature, 2020, pp. 2143–74, doi:10.1007/s11005-020-01286-w. short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174. date_created: 2020-03-23T11:11:47Z date_published: 2020-03-12T00:00:00Z date_updated: 2023-09-05T15:14:50Z day: '12' ddc: - '510' department: - _id: RoSe doi: 10.1007/s11005-020-01286-w ec_funded: 1 external_id: isi: - '000551556000006' file: - access_level: open_access checksum: 3bdd41f10ad947b67a45b98f507a7d4a content_type: application/pdf creator: dernst date_created: 2020-11-20T12:04:26Z date_updated: 2020-11-20T12:04:26Z file_id: '8784' file_name: 2020_LettersMathPhysics_Rademacher.pdf file_size: 478683 relation: main_file success: 1 file_date_updated: 2020-11-20T12:04:26Z has_accepted_license: '1' intvolume: ' 110' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 2143-2174 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: 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: Central limit theorem for Bose gases interacting through singular potentials 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: 110 year: '2020' ... --- _id: '7514' abstract: - lang: eng text: "We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case.\r\nWe motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Simon full_name: Mayer, Simon id: 30C4630A-F248-11E8-B48F-1D18A9856A87 last_name: Mayer citation: ama: Mayer S. The free energy of a dilute two-dimensional Bose gas. 2020. doi:10.15479/AT:ISTA:7514 apa: Mayer, S. (2020). The free energy of a dilute two-dimensional Bose gas. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:7514 chicago: Mayer, Simon. “The Free Energy of a Dilute Two-Dimensional Bose Gas.” Institute of Science and Technology Austria, 2020. https://doi.org/10.15479/AT:ISTA:7514. ieee: S. Mayer, “The free energy of a dilute two-dimensional Bose gas,” Institute of Science and Technology Austria, 2020. ista: Mayer S. 2020. The free energy of a dilute two-dimensional Bose gas. Institute of Science and Technology Austria. mla: Mayer, Simon. The Free Energy of a Dilute Two-Dimensional Bose Gas. Institute of Science and Technology Austria, 2020, doi:10.15479/AT:ISTA:7514. short: S. Mayer, The Free Energy of a Dilute Two-Dimensional Bose Gas, Institute of Science and Technology Austria, 2020. date_created: 2020-02-24T09:17:27Z date_published: 2020-02-24T00:00:00Z date_updated: 2023-09-07T13:12:42Z day: '24' ddc: - '510' degree_awarded: PhD department: - _id: RoSe - _id: GradSch doi: 10.15479/AT:ISTA:7514 ec_funded: 1 file: - access_level: open_access checksum: b4de7579ddc1dbdd44ff3f17c48395f6 content_type: application/pdf creator: dernst date_created: 2020-02-24T09:15:06Z date_updated: 2020-07-14T12:47:59Z file_id: '7515' file_name: thesis.pdf file_size: 1563429 relation: main_file - access_level: closed checksum: ad7425867b52d7d9e72296e87bc9cb67 content_type: application/x-zip-compressed creator: dernst date_created: 2020-02-24T09:15:16Z date_updated: 2020-07-14T12:47:59Z file_id: '7516' file_name: thesis_source.zip file_size: 2028038 relation: source_file file_date_updated: 2020-07-14T12:47:59Z has_accepted_license: '1' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: '148' 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: '7524' 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: The free energy of a dilute two-dimensional 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: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2020' ... --- _id: '8587' abstract: - lang: eng text: Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born–Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules. acknowledgement: We are grateful to Areg Ghazaryan for valuable discussions. M.L. acknowledges support from the Austrian Science Fund (FWF) under Project No. P29902-N27 and from the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). G.B. acknowledges support from the Austrian Science Fund (FWF) under Project No. M2461-N27. A.D. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the European Research Council (ERC) Grant Agreement No. 694227 and under the Marie Sklodowska-Curie Grant Agreement No. 836146. R.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868. article_number: '164302' article_processing_charge: No article_type: original author: - first_name: Xiang full_name: Li, Xiang id: 4B7E523C-F248-11E8-B48F-1D18A9856A87 last_name: Li - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 - first_name: Giacomo full_name: Bighin, Giacomo id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87 last_name: Bighin orcid: 0000-0001-8823-9777 - first_name: Richard full_name: Schmidt, Richard last_name: Schmidt - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: Andreas full_name: Deuchert, Andreas id: 4DA65CD0-F248-11E8-B48F-1D18A9856A87 last_name: Deuchert orcid: 0000-0003-3146-6746 citation: ama: Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. Intermolecular forces and correlations mediated by a phonon bath. The Journal of Chemical Physics. 2020;152(16). doi:10.1063/1.5144759 apa: Li, X., Yakaboylu, E., Bighin, G., Schmidt, R., Lemeshko, M., & Deuchert, A. (2020). Intermolecular forces and correlations mediated by a phonon bath. The Journal of Chemical Physics. AIP Publishing. https://doi.org/10.1063/1.5144759 chicago: Li, Xiang, Enderalp Yakaboylu, Giacomo Bighin, Richard Schmidt, Mikhail Lemeshko, and Andreas Deuchert. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” The Journal of Chemical Physics. AIP Publishing, 2020. https://doi.org/10.1063/1.5144759. ieee: X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, and A. Deuchert, “Intermolecular forces and correlations mediated by a phonon bath,” The Journal of Chemical Physics, vol. 152, no. 16. AIP Publishing, 2020. ista: Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. 2020. Intermolecular forces and correlations mediated by a phonon bath. The Journal of Chemical Physics. 152(16), 164302. mla: Li, Xiang, et al. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” The Journal of Chemical Physics, vol. 152, no. 16, 164302, AIP Publishing, 2020, doi:10.1063/1.5144759. short: X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, A. Deuchert, The Journal of Chemical Physics 152 (2020). date_created: 2020-09-30T10:33:17Z date_published: 2020-04-27T00:00:00Z date_updated: 2023-09-07T13:16:42Z day: '27' department: - _id: MiLe - _id: RoSe doi: 10.1063/1.5144759 ec_funded: 1 external_id: arxiv: - '1912.02658' isi: - '000530448300001' intvolume: ' 152' isi: 1 issue: '16' keyword: - Physical and Theoretical Chemistry - General Physics and Astronomy language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1912.02658 month: '04' oa: 1 oa_version: Preprint project: - _id: 26031614-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P29902 name: Quantum rotations in the presence of a many-body environment - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' - _id: 26986C82-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02641 name: A path-integral approach to composite impurities - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: The Journal of Chemical Physics publication_identifier: eissn: - 1089-7690 issn: - 0021-9606 publication_status: published publisher: AIP Publishing quality_controlled: '1' related_material: record: - id: '8958' relation: dissertation_contains status: public status: public title: Intermolecular forces and correlations mediated by a phonon bath type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 152 year: '2020' ... --- _id: '9781' abstract: - lang: eng text: We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum. acknowledgement: We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227. 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: 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. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 2020;52(1):605-622. doi:10.1137/19m126284x apa: Feliciangeli, D., & Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics . https://doi.org/10.1137/19m126284x chicago: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics , 2020. https://doi.org/10.1137/19m126284x. ieee: D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” SIAM Journal on Mathematical Analysis, vol. 52, no. 1. Society for Industrial & Applied Mathematics , pp. 605–622, 2020. ista: Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622. mla: Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” SIAM Journal on Mathematical Analysis, vol. 52, no. 1, Society for Industrial & Applied Mathematics , 2020, pp. 605–22, doi:10.1137/19m126284x. short: D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622. date_created: 2021-08-06T07:34:16Z date_published: 2020-02-12T00:00:00Z date_updated: 2023-09-07T13:30:11Z day: '12' ddc: - '510' department: - _id: RoSe doi: 10.1137/19m126284x ec_funded: 1 external_id: arxiv: - '1904.08647 ' isi: - '000546967700022' has_accepted_license: '1' intvolume: ' 52' isi: 1 issue: '1' keyword: - Applied Mathematics - Computational Mathematics - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1904.08647 month: '02' oa: 1 oa_version: Preprint page: 605-622 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: SIAM Journal on Mathematical Analysis publication_identifier: eissn: - 1095-7154 issn: - 0036-1410 publication_status: published publisher: 'Society for Industrial & Applied Mathematics ' quality_controlled: '1' related_material: record: - id: '9733' relation: dissertation_contains status: public scopus_import: '1' status: public title: Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 52 year: '2020' ... --- _id: '8705' abstract: - lang: eng text: We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model. 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. 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: 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. Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. Annales Henri Poincare. 2020;21(12):4003-4025. doi:10.1007/s00023-020-00969-3 apa: Mysliwy, K., & Seiringer, R. (2020). Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-020-00969-3 chicago: Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” Annales Henri Poincare. Springer Nature, 2020. https://doi.org/10.1007/s00023-020-00969-3. ieee: K. Mysliwy and R. Seiringer, “Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit,” Annales Henri Poincare, vol. 21, no. 12. Springer Nature, pp. 4003–4025, 2020. ista: Mysliwy K, Seiringer R. 2020. Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. Annales Henri Poincare. 21(12), 4003–4025. mla: Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” Annales Henri Poincare, vol. 21, no. 12, Springer Nature, 2020, pp. 4003–25, doi:10.1007/s00023-020-00969-3. short: K. Mysliwy, R. Seiringer, Annales Henri Poincare 21 (2020) 4003–4025. date_created: 2020-10-25T23:01:19Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-09-07T13:43:51Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s00023-020-00969-3 ec_funded: 1 external_id: arxiv: - '2003.12371' isi: - '000578111800002' file: - access_level: open_access checksum: c12c9c1e6f08def245e42f3cb1d83827 content_type: application/pdf creator: cziletti date_created: 2020-10-27T12:49:04Z date_updated: 2020-10-27T12:49:04Z file_id: '8711' file_name: 2020_Annales_Mysliwy.pdf file_size: 469831 relation: main_file success: 1 file_date_updated: 2020-10-27T12:49:04Z has_accepted_license: '1' intvolume: ' 21' isi: 1 issue: '12' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 4003-4025 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 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: Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the 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: 21 year: '2020' ...