[{"related_material":{"record":[{"id":"12911","relation":"later_version","status":"public"},{"status":"public","relation":"dissertation_contains","id":"9733"},{"status":"public","relation":"dissertation_contains","id":"10030"}]},"project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"date_created":"2021-08-06T09:07:12Z","article_processing_charge":"No","month":"07","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"language":[{"iso":"eng"}],"publication_status":"draft","article_number":"2106.11217","doi":"10.48550/arXiv.2106.11217","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"type":"preprint","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","oa":1,"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","first_name":"Dario","orcid":"0000-0003-0754-8530"},{"first_name":"Augusto","full_name":"Gerolin, Augusto","last_name":"Gerolin"},{"last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","full_name":"Portinale, Lorenzo","first_name":"Lorenzo"}],"publication":"arXiv","external_id":{"arxiv":["2106.11217"]},"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].","citation":{"apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>arXiv</i>. .","ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, 2106.11217, doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>."},"year":"2021","arxiv":1,"day":"21","oa_version":"Preprint","_id":"9792","status":"public","fulldoi":"https://doi.org/10.48550/arXiv.2106.11217","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510"],"date_published":"2021-07-21T00:00:00Z","has_accepted_license":"1","ec_funded":1,"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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-04-08T07:00:03Z"},{"intvolume":"        62","file":[{"success":1,"file_id":"10188","date_created":"2021-10-27T12:57:06Z","file_size":4352640,"file_name":"2021_JMathPhy_Lauritsen.pdf","access_level":"open_access","checksum":"d035be2b894c4d50d90ac5ce252e27cd","relation":"main_file","creator":"cziletti","date_updated":"2021-10-27T12:57:06Z","content_type":"application/pdf"}],"issue":"8","external_id":{"arxiv":["2103.07975"],"isi":["000683960800003"]},"oa_version":"Published Version","status":"public","_id":"9891","publisher":"AIP Publishing","citation":{"short":"A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).","mla":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>.","chicago":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2021. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>.","apa":"Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0053494\">https://doi.org/10.1063/5.0053494</a>","ieee":"A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 8. AIP Publishing, 2021.","ama":"Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. <i>Journal of Mathematical Physics</i>. 2021;62(8). doi:<a href=\"https://doi.org/10.1063/5.0053494\">10.1063/5.0053494</a>","ista":"Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305."},"year":"2021","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.","isi":1,"day":"01","arxiv":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1063/5.0053494","article_type":"original","has_accepted_license":"1","date_published":"2021-08-01T00:00:00Z","ddc":["530"],"date_updated":"2024-10-09T21:00:48Z","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."}],"file_date_updated":"2021-10-27T12:57:06Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","date_created":"2021-08-12T07:08:36Z","quality_controlled":"1","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"volume":62,"language":[{"iso":"eng"}],"month":"08","type":"journal_article","doi":"10.1063/5.0053494","oa":1,"title":"Floating Wigner crystal and periodic jellium configurations","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"article_number":"083305","scopus_import":"1","corr_author":"1","author":[{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"publication":"Journal of Mathematical Physics"},{"type":"dissertation","doi":"10.15479/at:ista:9733","title":"The polaron at strong coupling","oa":1,"publication_identifier":{"issn":["2663-337X"]},"corr_author":"1","author":[{"orcid":"0000-0003-0754-8530","first_name":"Dario","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","date_created":"2021-07-27T15:48:30Z","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"9787"},{"status":"public","id":"9792","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"9791"},{"status":"public","id":"9225","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"9781","status":"public"}]},"degree_awarded":"PhD","project":[{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"publication_status":"published","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"language":[{"iso":"eng"}],"page":"180","month":"08","tmp":{"image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","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)"},"fulldoi":"https://doi.org/10.15479/at:ista:9733","date_published":"2021-08-20T00:00:00Z","has_accepted_license":"1","ddc":["515","519","539"],"OA_place":"publisher","alternative_title":["ISTA Thesis"],"date_updated":"2026-07-06T14:02:25Z","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2022-03-10T12:13:57Z","ec_funded":1,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file":[{"access_level":"open_access","checksum":"e88bb8ca43948abe060eb2d2fa719881","relation":"main_file","creator":"dfelicia","content_type":"application/pdf","date_updated":"2021-09-06T09:28:56Z","file_id":"9944","file_size":1958710,"date_created":"2021-08-19T14:03:48Z","file_name":"Thesis_FeliciangeliA.pdf"},{"date_created":"2021-08-19T14:06:35Z","file_size":3771669,"file_name":"thesis.7z","file_id":"9945","creator":"dfelicia","date_updated":"2022-03-10T12:13:57Z","content_type":"application/octet-stream","checksum":"72810843abee83705853505b3f8348aa","access_level":"closed","relation":"source_file"}],"oa_version":"Published Version","status":"public","_id":"9733","publisher":"Institute of Science and Technology Austria","citation":{"chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>.","mla":"Feliciangeli, Dario. <i>The Polaron at Strong Coupling</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","apa":"Feliciangeli, D. (2021). <i>The polaron at strong coupling</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021."},"year":"2021","supervisor":[{"full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"},{"last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","first_name":"Jan","orcid":"0000-0002-0845-1338"}],"day":"20"},{"corr_author":"1","scopus_import":"1","publication":"Analysis and PDE","author":[{"orcid":"0000-0002-0495-6822","first_name":"Nikolai K","full_name":"Leopold, Nikolai K","last_name":"Leopold","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5059-4466","first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","last_name":"Rademacher","full_name":"Rademacher, Simone Anna Elvira"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication_identifier":{"eissn":["1948-206X"],"issn":["2157-5045"]},"oa":1,"title":"The Landau–Pekar equations: Adiabatic theorem and accuracy","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.12532"}],"doi":"10.2140/APDE.2021.14.2079","type":"journal_article","page":"2079-2100","language":[{"iso":"eng"}],"volume":14,"department":[{"_id":"RoSe"}],"publication_status":"published","month":"11","date_created":"2022-02-06T23:01:33Z","article_processing_charge":"No","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"quality_controlled":"1","date_updated":"2026-08-12T08:46:52Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"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."}],"date_published":"2021-11-10T00:00:00Z","fulldoi":"https://doi.org/10.2140/APDE.2021.14.2079","article_type":"original","status":"public","_id":"10738","oa_version":"Preprint","arxiv":1,"day":"10","isi":1,"year":"2021","citation":{"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.","ama":"Leopold NK, Rademacher SAE, Schlein B, Seiringer R. The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. 2021;14(7):2079-2100. doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>","ieee":"N. K. Leopold, S. A. E. Rademacher, B. Schlein, and R. Seiringer, “The Landau–Pekar equations: Adiabatic theorem and accuracy,” <i>Analysis and PDE</i>, vol. 14, no. 7. Mathematical Sciences Publishers, pp. 2079–2100, 2021.","apa":"Leopold, N. K., Rademacher, S. A. E., Schlein, B., &#38; Seiringer, R. (2021). The Landau–Pekar equations: Adiabatic theorem and accuracy. <i>Analysis and PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>","chicago":"Leopold, Nikolai K, Simone Anna Elvira Rademacher, Benjamin Schlein, and Robert Seiringer. “The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">https://doi.org/10.2140/APDE.2021.14.2079</a>.","short":"N.K. Leopold, S.A.E. Rademacher, B. Schlein, R. Seiringer, Analysis and PDE 14 (2021) 2079–2100.","mla":"Leopold, Nikolai K., et al. “The Landau–Pekar Equations: Adiabatic Theorem and Accuracy.” <i>Analysis and PDE</i>, vol. 14, no. 7, Mathematical Sciences Publishers, 2021, pp. 2079–100, doi:<a href=\"https://doi.org/10.2140/APDE.2021.14.2079\">10.2140/APDE.2021.14.2079</a>."},"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","publisher":"Mathematical Sciences Publishers","external_id":{"isi":["000733976600004"],"arxiv":["1904.12532"]},"issue":"7","intvolume":"        14"},{"article_processing_charge":"Yes (via OA deal)","date_created":"2020-03-23T11:11:47Z","quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","volume":110,"department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"page":"2143-2174","month":"03","type":"journal_article","doi":"10.1007/s11005-020-01286-w","title":"Central limit theorem for Bose gases interacting through singular potentials","oa":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"scopus_import":"1","corr_author":"1","author":[{"orcid":"0000-0001-5059-4466","first_name":"Simone Anna Elvira","last_name":"Rademacher","id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira"}],"publication":"Letters in Mathematical Physics","intvolume":"       110","file":[{"checksum":"3bdd41f10ad947b67a45b98f507a7d4a","access_level":"open_access","relation":"main_file","date_updated":"2020-11-20T12:04:26Z","content_type":"application/pdf","creator":"dernst","success":1,"file_id":"8784","file_name":"2020_LettersMathPhysics_Rademacher.pdf","date_created":"2020-11-20T12:04:26Z","file_size":478683}],"external_id":{"isi":["000551556000006"]},"oa_version":"Published Version","status":"public","_id":"7611","publisher":"Springer Nature","citation":{"apa":"Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>","ieee":"S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through singular potentials,” <i>Letters in Mathematical Physics</i>, vol. 110. Springer Nature, pp. 2143–2174, 2020.","ama":"Rademacher SAE. Central limit theorem for Bose gases interacting through singular potentials. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>","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.” <i>Letters in Mathematical Physics</i>, vol. 110, Springer Nature, 2020, pp. 2143–74, doi:<a href=\"https://doi.org/10.1007/s11005-020-01286-w\">10.1007/s11005-020-01286-w</a>.","short":"S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.","chicago":"Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11005-020-01286-w\">https://doi.org/10.1007/s11005-020-01286-w</a>."},"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.","year":"2020","isi":1,"day":"12","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1007/s11005-020-01286-w","article_type":"original","date_published":"2020-03-12T00:00:00Z","has_accepted_license":"1","ddc":["510"],"date_updated":"2025-04-14T07:44:03Z","file_date_updated":"2020-11-20T12:04:26Z","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."}],"ec_funded":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","fulldoi":"https://doi.org/10.1007/s00205-020-01489-4","has_accepted_license":"1","date_published":"2020-03-09T00:00:00Z","ddc":["510"],"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"file_date_updated":"2020-11-20T13:17:42Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2025-04-14T07:27:00Z","intvolume":"       236","file":[{"relation":"main_file","checksum":"b645fb64bfe95bbc05b3eea374109a9c","access_level":"open_access","creator":"dernst","date_updated":"2020-11-20T13:17:42Z","content_type":"application/pdf","file_id":"8785","success":1,"file_size":704633,"date_created":"2020-11-20T13:17:42Z","file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf"}],"issue":"6","external_id":{"isi":["000519415000001"],"arxiv":["1901.11363"]},"publisher":"Springer Nature","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.","year":"2020","citation":{"ama":"Deuchert A, Seiringer R. Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. 2020;236(6):1217-1271. doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>","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.","apa":"Deuchert, A., &#38; Seiringer, R. (2020). Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>","ieee":"A. Deuchert and R. Seiringer, “Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6. Springer Nature, pp. 1217–1271, 2020.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01489-4\">https://doi.org/10.1007/s00205-020-01489-4</a>.","short":"A. Deuchert, R. Seiringer, Archive for Rational Mechanics and Analysis 236 (2020) 1217–1271.","mla":"Deuchert, Andreas, and Robert Seiringer. “Gross-Pitaevskii Limit of a Homogeneous Bose Gas at Positive Temperature.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 236, no. 6, Springer Nature, 2020, pp. 1217–71, doi:<a href=\"https://doi.org/10.1007/s00205-020-01489-4\">10.1007/s00205-020-01489-4</a>."},"isi":1,"arxiv":1,"day":"09","oa_version":"Published Version","status":"public","_id":"7650","type":"journal_article","doi":"10.1007/s00205-020-01489-4","oa":1,"title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"author":[{"full_name":"Deuchert, Andreas","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","last_name":"Deuchert","first_name":"Andreas","orcid":"0000-0003-3146-6746"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication":"Archive for Rational Mechanics and Analysis","scopus_import":"1","corr_author":"1","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2020-04-08T15:18:03Z","month":"03","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"volume":236,"page":"1217-1271"},{"intvolume":"         8","file":[{"access_level":"open_access","checksum":"8a64da99d107686997876d7cad8cfe1e","relation":"main_file","date_updated":"2020-07-14T12:48:03Z","content_type":"application/pdf","creator":"dernst","file_id":"7797","file_name":"2020_ForumMath_Deuchert.pdf","file_size":692530,"date_created":"2020-05-04T12:02:41Z"}],"external_id":{"isi":["000527342000001"],"arxiv":["1910.03372"]},"oa_version":"Published Version","_id":"7790","status":"public","publisher":"Cambridge University Press","citation":{"ama":"Deuchert A, Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. 2020;8. doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>","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.","ieee":"A. Deuchert, S. Mayer, and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. I. Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 8. Cambridge University Press, 2020.","apa":"Deuchert, A., Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. I. Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>","chicago":"Deuchert, Andreas, Simon Mayer, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2020. <a href=\"https://doi.org/10.1017/fms.2020.17\">https://doi.org/10.1017/fms.2020.17</a>.","short":"A. Deuchert, S. Mayer, R. Seiringer, Forum of Mathematics, Sigma 8 (2020).","mla":"Deuchert, Andreas, et al. “The Free Energy of the Two-Dimensional Dilute Bose Gas. I. Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 8, e20, Cambridge University Press, 2020, doi:<a href=\"https://doi.org/10.1017/fms.2020.17\">10.1017/fms.2020.17</a>."},"year":"2020","isi":1,"arxiv":1,"day":"14","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","fulldoi":"https://doi.org/10.1017/fms.2020.17","date_published":"2020-03-14T00:00:00Z","has_accepted_license":"1","ddc":["510"],"date_updated":"2026-04-03T09:30:21Z","ec_funded":1,"file_date_updated":"2020-07-14T12:48:03Z","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 𝜌 and inverse temperature 𝛽 differs from the one of the noninteracting system by the correction term 𝜋𝜌𝜌𝛽𝛽 . Here, is the scattering length of the interaction potential, and 𝛽 is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit 𝜌 and if 𝛽𝜌 ."}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","article_processing_charge":"No","date_created":"2020-05-03T22:00:48Z","quality_controlled":"1","related_material":{"record":[{"relation":"earlier_version","id":"7524","status":"public"}]},"project":[{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"publication_status":"published","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"volume":8,"month":"03","type":"journal_article","doi":"10.1017/fms.2020.17","title":"The free energy of the two-dimensional dilute Bose gas. I. Lower bound","oa":1,"publication_identifier":{"eissn":["2050-5094"]},"article_number":"e20","scopus_import":"1","corr_author":"1","author":[{"full_name":"Deuchert, Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","first_name":"Andreas","orcid":"0000-0003-3146-6746"},{"full_name":"Mayer, Simon","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","last_name":"Mayer","first_name":"Simon"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"publication":"Forum of Mathematics, Sigma"},{"date_published":"2020-10-01T00:00:00Z","has_accepted_license":"1","ddc":["530"],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1007/s10955-020-02586-0","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"file_date_updated":"2020-11-25T15:05:04Z","abstract":[{"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.","lang":"eng"}],"date_updated":"2025-07-10T11:55:04Z","external_id":{"arxiv":["2001.07144"],"isi":["000543030000002"]},"intvolume":"       181","file":[{"file_id":"8812","success":1,"date_created":"2020-11-25T15:05:04Z","file_size":404778,"file_name":"2020_JourStatPhysics_Seiringer.pdf","relation":"main_file","access_level":"open_access","checksum":"5cbeef52caf18d0d952f17fed7b5545a","creator":"dernst","content_type":"application/pdf","date_updated":"2020-11-25T15:05:04Z"}],"isi":1,"arxiv":1,"day":"01","publisher":"Springer","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. ","year":"2020","citation":{"chicago":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>.","mla":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>, vol. 181, Springer, 2020, pp. 448–64, doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>.","short":"R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.","ama":"Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. 2020;181:448-464. doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>","ista":"Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464.","ieee":"R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” <i>Journal of Statistical Physics</i>, vol. 181. Springer, pp. 448–464, 2020.","apa":"Seiringer, R., &#38; Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>"},"status":"public","_id":"8091","oa_version":"Published Version","oa":1,"title":"Emergence of Haldane pseudo-potentials in systems with short-range interactions","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"type":"journal_article","doi":"10.1007/s10955-020-02586-0","publication":"Journal of Statistical Physics","author":[{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"corr_author":"1","scopus_import":"1","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"}],"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","date_created":"2020-07-05T22:00:46Z","month":"10","page":"448-464","publication_status":"published","language":[{"iso":"eng"}],"volume":181,"department":[{"_id":"RoSe"}]},{"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","date_created":"2020-07-18T15:06:35Z","article_processing_charge":"Yes (via OA deal)","month":"11","page":"541-606","volume":238,"language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"title":"Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons","oa":1,"doi":"10.1007/s00205-020-01548-w","type":"journal_article","publication":"Archive for Rational Mechanics and Analysis","author":[{"full_name":"Bossmann, Lea","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","first_name":"Lea","orcid":"0000-0002-6854-1343"}],"corr_author":"1","scopus_import":"1","external_id":{"isi":["000550164400001"],"arxiv":["1907.04547"]},"issue":"11","file":[{"relation":"main_file","access_level":"open_access","checksum":"cc67a79a67bef441625fcb1cd031db3d","content_type":"application/pdf","date_updated":"2020-12-02T08:50:38Z","creator":"dernst","file_id":"8826","success":1,"file_name":"2020_ArchiveRatMech_Bossmann.pdf","date_created":"2020-12-02T08:50:38Z","file_size":942343}],"intvolume":"       238","arxiv":1,"day":"01","isi":1,"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.","citation":{"short":"L. Bossmann, Archive for Rational Mechanics and Analysis 238 (2020) 541–606.","mla":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11, Springer Nature, 2020, pp. 541–606, doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>.","chicago":"Bossmann, Lea. “Derivation of the 2d Gross–Pitaevskii Equation for Strongly Confined 3d Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>.","apa":"Bossmann, L. (2020). Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-020-01548-w\">https://doi.org/10.1007/s00205-020-01548-w</a>","ieee":"L. Bossmann, “Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 238, no. 11. Springer Nature, pp. 541–606, 2020.","ama":"Bossmann L. Derivation of the 2d Gross–Pitaevskii equation for strongly confined 3d Bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2020;238(11):541-606. doi:<a href=\"https://doi.org/10.1007/s00205-020-01548-w\">10.1007/s00205-020-01548-w</a>","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."},"year":"2020","publisher":"Springer Nature","status":"public","_id":"8130","oa_version":"Published Version","ddc":["510"],"date_published":"2020-11-01T00:00:00Z","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s00205-020-01548-w","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file_date_updated":"2020-12-02T08:50:38Z","ec_funded":1,"abstract":[{"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.","lang":"eng"}],"date_updated":"2025-04-14T07:44:05Z"},{"issue":"6","external_id":{"isi":["000544595100001"],"arxiv":["2002.08281"]},"intvolume":"        61","isi":1,"arxiv":1,"day":"22","publisher":"AIP Publishing","citation":{"mla":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6, 061901, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>.","short":"S. Mayer, R. Seiringer, Journal of Mathematical Physics 61 (2020).","chicago":"Mayer, Simon, and Robert Seiringer. “The Free Energy of the Two-Dimensional Dilute Bose Gas. II. Upper Bound.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>.","ieee":"S. Mayer and R. Seiringer, “The free energy of the two-dimensional dilute Bose gas. II. Upper bound,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 6. AIP Publishing, 2020.","apa":"Mayer, S., &#38; Seiringer, R. (2020). The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0005950\">https://doi.org/10.1063/5.0005950</a>","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.","ama":"Mayer S, Seiringer R. The free energy of the two-dimensional dilute Bose gas. II. Upper bound. <i>Journal of Mathematical Physics</i>. 2020;61(6). doi:<a href=\"https://doi.org/10.1063/5.0005950\">10.1063/5.0005950</a>"},"year":"2020","_id":"8134","status":"public","oa_version":"Preprint","date_published":"2020-06-22T00:00:00Z","fulldoi":"https://doi.org/10.1063/5.0005950","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"date_updated":"2025-07-10T11:55:05Z","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","article_processing_charge":"No","date_created":"2020-07-19T22:00:59Z","month":"06","publication_status":"published","volume":61,"department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"article_number":"061901","title":"The free energy of the two-dimensional dilute Bose gas. II. Upper bound","oa":1,"publication_identifier":{"issn":["0022-2488"]},"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.08281"}],"doi":"10.1063/5.0005950","publication":"Journal of Mathematical Physics","author":[{"first_name":"Simon","full_name":"Mayer, Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"corr_author":"1","scopus_import":"1"},{"publication":"The Journal of Chemical Physics","author":[{"first_name":"Xiang","full_name":"Li, Xiang","id":"4B7E523C-F248-11E8-B48F-1D18A9856A87","last_name":"Li"},{"id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","last_name":"Yakaboylu","full_name":"Yakaboylu, Enderalp","orcid":"0000-0001-5973-0874","first_name":"Enderalp"},{"full_name":"Bighin, Giacomo","id":"4CA96FD4-F248-11E8-B48F-1D18A9856A87","last_name":"Bighin","orcid":"0000-0001-8823-9777","first_name":"Giacomo"},{"first_name":"Richard","last_name":"Schmidt","full_name":"Schmidt, Richard"},{"full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","last_name":"Lemeshko","orcid":"0000-0002-6990-7802","first_name":"Mikhail"},{"orcid":"0000-0003-3146-6746","first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87"}],"corr_author":"1","article_number":"164302","pmid":1,"publication_identifier":{"eissn":["1089-7690"],"issn":["0021-9606"]},"oa":1,"title":"Intermolecular forces and correlations mediated by a phonon bath","main_file_link":[{"url":"https://arxiv.org/abs/1912.02658","open_access":"1"}],"doi":"10.1063/1.5144759","type":"journal_article","month":"04","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"language":[{"iso":"eng"}],"volume":152,"publication_status":"published","project":[{"_id":"26031614-B435-11E9-9278-68D0E5697425","name":"Quantum rotations in the presence of a many-body environment","call_identifier":"FWF","grant_number":"P29902"},{"name":"Angulon: physics and applications of a new quasiparticle","_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"801770"},{"grant_number":"M02641","call_identifier":"FWF","name":"A path-integral approach to composite impurities","_id":"26986C82-B435-11E9-9278-68D0E5697425"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"related_material":{"record":[{"status":"public","id":"8958","relation":"dissertation_contains"}]},"quality_controlled":"1","date_created":"2020-09-30T10:33:17Z","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"ec_funded":1,"date_updated":"2026-04-08T07:26:09Z","date_published":"2020-04-27T00:00:00Z","fulldoi":"https://doi.org/10.1063/1.5144759","article_type":"original","keyword":["Physical and Theoretical Chemistry","General Physics and Astronomy"],"arxiv":1,"day":"27","isi":1,"year":"2020","citation":{"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.","ama":"Li X, Yakaboylu E, Bighin G, Schmidt R, Lemeshko M, Deuchert A. Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. 2020;152(16). doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>","ieee":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, and A. Deuchert, “Intermolecular forces and correlations mediated by a phonon bath,” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16. AIP Publishing, 2020.","apa":"Li, X., Yakaboylu, E., Bighin, G., Schmidt, R., Lemeshko, M., &#38; Deuchert, A. (2020). Intermolecular forces and correlations mediated by a phonon bath. <i>The Journal of Chemical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>","chicago":"Li, Xiang, Enderalp Yakaboylu, Giacomo Bighin, Richard Schmidt, Mikhail Lemeshko, and Andreas Deuchert. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/1.5144759\">https://doi.org/10.1063/1.5144759</a>.","mla":"Li, Xiang, et al. “Intermolecular Forces and Correlations Mediated by a Phonon Bath.” <i>The Journal of Chemical Physics</i>, vol. 152, no. 16, 164302, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/1.5144759\">10.1063/1.5144759</a>.","short":"X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, A. Deuchert, The Journal of Chemical Physics 152 (2020)."},"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.","publisher":"AIP Publishing","_id":"8587","status":"public","oa_version":"Preprint","external_id":{"pmid":["32357791"],"arxiv":["1912.02658"],"isi":["000530448300001"]},"issue":"16","intvolume":"       152"},{"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"11473"}]},"quality_controlled":"1","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2020-10-25T23:01:19Z","month":"12","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"volume":21,"page":"4003-4025","type":"journal_article","doi":"10.1007/s00023-020-00969-3","title":"Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit","oa":1,"publication_identifier":{"issn":["1424-0637"]},"author":[{"first_name":"Krzysztof","full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","last_name":"Mysliwy"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"publication":"Annales Henri Poincare","scopus_import":"1","corr_author":"1","intvolume":"        21","file":[{"relation":"main_file","access_level":"open_access","checksum":"c12c9c1e6f08def245e42f3cb1d83827","date_updated":"2020-10-27T12:49:04Z","content_type":"application/pdf","creator":"cziletti","file_id":"8711","success":1,"file_name":"2020_Annales_Mysliwy.pdf","file_size":469831,"date_created":"2020-10-27T12:49:04Z"}],"issue":"12","external_id":{"arxiv":["2003.12371"],"isi":["000578111800002"]},"publisher":"Springer Nature","year":"2020","citation":{"chicago":"Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” <i>Annales Henri Poincare</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00023-020-00969-3\">https://doi.org/10.1007/s00023-020-00969-3</a>.","short":"K. Mysliwy, R. Seiringer, Annales Henri Poincare 21 (2020) 4003–4025.","mla":"Mysliwy, Krzysztof, and Robert Seiringer. “Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit.” <i>Annales Henri Poincare</i>, vol. 21, no. 12, Springer Nature, 2020, pp. 4003–25, doi:<a href=\"https://doi.org/10.1007/s00023-020-00969-3\">10.1007/s00023-020-00969-3</a>.","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.","ama":"Mysliwy K, Seiringer R. Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. <i>Annales Henri Poincare</i>. 2020;21(12):4003-4025. doi:<a href=\"https://doi.org/10.1007/s00023-020-00969-3\">10.1007/s00023-020-00969-3</a>","apa":"Mysliwy, K., &#38; Seiringer, R. (2020). Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-020-00969-3\">https://doi.org/10.1007/s00023-020-00969-3</a>","ieee":"K. Mysliwy and R. Seiringer, “Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit,” <i>Annales Henri Poincare</i>, vol. 21, no. 12. Springer Nature, pp. 4003–4025, 2020."},"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)","isi":1,"arxiv":1,"day":"01","oa_version":"Published Version","status":"public","_id":"8705","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1007/s00023-020-00969-3","article_type":"original","has_accepted_license":"1","date_published":"2020-12-01T00:00:00Z","ddc":["530"],"file_date_updated":"2020-10-27T12:49:04Z","ec_funded":1,"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."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_updated":"2026-04-07T14:14:51Z"},{"month":"10","publication_status":"published","department":[{"_id":"MiLe"},{"_id":"RoSe"}],"volume":102,"language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"grant_number":"801770","call_identifier":"H2020","_id":"2688CF98-B435-11E9-9278-68D0E5697425","name":"Angulon: physics and applications of a new quasiparticle"}],"article_processing_charge":"No","date_created":"2020-11-18T07:34:17Z","author":[{"last_name":"Yakaboylu","id":"38CB71F6-F248-11E8-B48F-1D18A9856A87","full_name":"Yakaboylu, Enderalp","orcid":"0000-0001-5973-0874","first_name":"Enderalp"},{"first_name":"Areg","orcid":"0000-0001-9666-3543","last_name":"Ghazaryan","id":"4AF46FD6-F248-11E8-B48F-1D18A9856A87","full_name":"Ghazaryan, Areg"},{"first_name":"D.","full_name":"Lundholm, D.","last_name":"Lundholm"},{"full_name":"Rougerie, N.","last_name":"Rougerie","first_name":"N."},{"full_name":"Lemeshko, Mikhail","last_name":"Lemeshko","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6990-7802","first_name":"Mikhail"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"publication":"Physical Review B","scopus_import":"1","article_number":"144109","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1912.07890","open_access":"1"}],"doi":"10.1103/physrevb.102.144109","title":"Quantum impurity model for anyons","oa":1,"publication_identifier":{"eissn":["2469-9969"],"issn":["2469-9950"]},"publisher":"American Physical Society","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).","year":"2020","citation":{"ieee":"E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, and R. Seiringer, “Quantum impurity model for anyons,” <i>Physical Review B</i>, vol. 102, no. 14. American Physical Society, 2020.","apa":"Yakaboylu, E., Ghazaryan, A., Lundholm, D., Rougerie, N., Lemeshko, M., &#38; Seiringer, R. (2020). Quantum impurity model for anyons. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.102.144109\">https://doi.org/10.1103/physrevb.102.144109</a>","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.","ama":"Yakaboylu E, Ghazaryan A, Lundholm D, Rougerie N, Lemeshko M, Seiringer R. Quantum impurity model for anyons. <i>Physical Review B</i>. 2020;102(14). doi:<a href=\"https://doi.org/10.1103/physrevb.102.144109\">10.1103/physrevb.102.144109</a>","mla":"Yakaboylu, Enderalp, et al. “Quantum Impurity Model for Anyons.” <i>Physical Review B</i>, vol. 102, no. 14, 144109, American Physical Society, 2020, doi:<a href=\"https://doi.org/10.1103/physrevb.102.144109\">10.1103/physrevb.102.144109</a>.","short":"E. Yakaboylu, A. Ghazaryan, D. Lundholm, N. Rougerie, M. Lemeshko, R. Seiringer, Physical Review B 102 (2020).","chicago":"Yakaboylu, Enderalp, Areg Ghazaryan, D. Lundholm, N. Rougerie, Mikhail Lemeshko, and Robert Seiringer. “Quantum Impurity Model for Anyons.” <i>Physical Review B</i>. American Physical Society, 2020. <a href=\"https://doi.org/10.1103/physrevb.102.144109\">https://doi.org/10.1103/physrevb.102.144109</a>."},"isi":1,"day":"01","arxiv":1,"oa_version":"Preprint","status":"public","_id":"8769","intvolume":"       102","issue":"14","external_id":{"arxiv":["1912.07890"],"isi":["000582563300001"]},"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."}],"ec_funded":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2025-04-14T07:26:54Z","fulldoi":"https://doi.org/10.1103/physrevb.102.144109","article_type":"original","date_published":"2020-10-01T00:00:00Z"},{"date_updated":"2025-04-14T07:27:00Z","ec_funded":1,"file_date_updated":"2020-07-14T12:47:35Z","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"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.1007/s00220-019-03505-5","article_type":"original","has_accepted_license":"1","date_published":"2020-03-01T00:00:00Z","ddc":["530"],"oa_version":"Published Version","_id":"6649","status":"public","publisher":"Springer Nature","citation":{"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,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>","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.","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. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>","mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","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.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>."},"year":"2020","isi":1,"day":"01","arxiv":1,"intvolume":"       374","file":[{"file_id":"6668","file_size":853289,"date_created":"2019-07-24T07:19:10Z","file_name":"2019_CommMathPhysics_Benedikter.pdf","access_level":"open_access","checksum":"f9dd6dd615a698f1d3636c4a092fed23","relation":"main_file","creator":"dernst","date_updated":"2020-07-14T12:47:35Z","content_type":"application/pdf"}],"external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"scopus_import":"1","corr_author":"1","author":[{"orcid":"0000-0002-1071-6091","first_name":"Niels P","last_name":"Benedikter","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","full_name":"Benedikter, Niels P"},{"last_name":"Nam","full_name":"Nam, Phan Thành","first_name":"Phan Thành"},{"last_name":"Porta","full_name":"Porta, Marcello","first_name":"Marcello"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"publication":"Communications in Mathematical Physics","type":"journal_article","doi":"10.1007/s00220-019-03505-5","oa":1,"title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"publication_status":"published","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"volume":374,"page":"2097–2150","month":"03","article_processing_charge":"No","date_created":"2019-07-18T13:30:04Z","quality_controlled":"1","project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"},{"call_identifier":"FWF","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"},{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}]},{"status":"public","_id":"6906","oa_version":"Preprint","isi":1,"day":"01","arxiv":1,"publisher":"Springer","citation":{"apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer, pp. 1311–1395, 2020.","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. 2020;376:1311-1395. doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 376, 1311–1395.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","mla":"Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer, 2020, pp. 1311–95, doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>.","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>."},"acknowledgement":"We would like to thank P. T. Nam and R. Seiringer for several useful discussions and\r\nfor suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”.","year":"2020","external_id":{"isi":["000536053300012"],"arxiv":["1812.03086"]},"intvolume":"       376","date_updated":"2025-04-14T07:27:00Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential."}],"date_published":"2020-06-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s00220-019-03555-9","article_type":"original","page":"1311-1395","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"}],"volume":376,"month":"06","article_processing_charge":"No","date_created":"2019-09-24T17:30:59Z","project":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","scopus_import":"1","publication":"Communications in Mathematical Physics","author":[{"first_name":"Chiara","full_name":"Boccato, Chiara","last_name":"Boccato","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Brennecke, Christian","last_name":"Brennecke","first_name":"Christian"},{"full_name":"Cenatiempo, Serena","last_name":"Cenatiempo","first_name":"Serena"},{"last_name":"Schlein","full_name":"Schlein, Benjamin","first_name":"Benjamin"}],"title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","oa":1,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1812.03086","open_access":"1"}],"doi":"10.1007/s00220-019-03555-9"},{"abstract":[{"text":"We consider the Fröhlich model of a polaron, and show that its effective mass diverges in thestrong coupling limit.","lang":"eng"}],"ec_funded":1,"file_date_updated":"2020-11-19T11:13:55Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2025-04-14T07:27:01Z","fulldoi":"https://doi.org/10.1007/s10955-019-02322-3","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"ddc":["510","530"],"has_accepted_license":"1","date_published":"2020-09-01T00:00:00Z","citation":{"ieee":"E. H. Lieb and R. Seiringer, “Divergence of the effective mass of a polaron in the strong coupling limit,” <i>Journal of Statistical Physics</i>, vol. 180. Springer Nature, pp. 23–33, 2020.","apa":"Lieb, E. H., &#38; Seiringer, R. (2020). Divergence of the effective mass of a polaron in the strong coupling limit. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-019-02322-3\">https://doi.org/10.1007/s10955-019-02322-3</a>","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.","ama":"Lieb EH, Seiringer R. Divergence of the effective mass of a polaron in the strong coupling limit. <i>Journal of Statistical Physics</i>. 2020;180:23-33. doi:<a href=\"https://doi.org/10.1007/s10955-019-02322-3\">10.1007/s10955-019-02322-3</a>","mla":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” <i>Journal of Statistical Physics</i>, vol. 180, Springer Nature, 2020, pp. 23–33, doi:<a href=\"https://doi.org/10.1007/s10955-019-02322-3\">10.1007/s10955-019-02322-3</a>.","short":"E.H. Lieb, R. Seiringer, Journal of Statistical Physics 180 (2020) 23–33.","chicago":"Lieb, Elliott H., and Robert Seiringer. “Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-019-02322-3\">https://doi.org/10.1007/s10955-019-02322-3</a>."},"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.","year":"2020","publisher":"Springer Nature","day":"01","isi":1,"oa_version":"Published Version","status":"public","_id":"7235","file":[{"relation":"main_file","access_level":"open_access","checksum":"1e67bee6728592f7bdcea2ad2d9366dc","creator":"dernst","date_updated":"2020-11-19T11:13:55Z","content_type":"application/pdf","file_id":"8774","success":1,"file_size":279749,"date_created":"2020-11-19T11:13:55Z","file_name":"2020_JourStatPhysics_Lieb.pdf"}],"intvolume":"       180","external_id":{"isi":["000556199700003"]},"author":[{"first_name":"Elliott H.","full_name":"Lieb, Elliott H.","last_name":"Lieb"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"publication":"Journal of Statistical Physics","scopus_import":"1","corr_author":"1","doi":"10.1007/s10955-019-02322-3","type":"journal_article","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"oa":1,"title":"Divergence of the effective mass of a polaron in the strong coupling limit","month":"09","language":[{"iso":"eng"}],"volume":180,"department":[{"_id":"RoSe"}],"publication_status":"published","page":"23-33","quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"}],"date_created":"2020-01-07T09:42:03Z","article_processing_charge":"Yes (via OA deal)"},{"corr_author":"1","scopus_import":"1","publication":"Journal of Statistical Physics","author":[{"orcid":"0000-0002-6854-1343","first_name":"Lea","last_name":"Bossmann","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425","full_name":"Bossmann, Lea"},{"first_name":"Nataša","last_name":"Pavlović","full_name":"Pavlović, Nataša"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"},{"last_name":"Soffer","full_name":"Soffer, Avy","first_name":"Avy"}],"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"oa":1,"title":"Higher order corrections to the mean-field description of the dynamics of interacting bosons","doi":"10.1007/s10955-020-02500-8","type":"journal_article","page":"1362-1396","language":[{"iso":"eng"}],"volume":178,"department":[{"_id":"RoSe"}],"publication_status":"published","month":"02","date_created":"2020-02-23T09:45:51Z","article_processing_charge":"Yes (via OA deal)","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"quality_controlled":"1","date_updated":"2025-04-14T07:44:03Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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."}],"file_date_updated":"2020-11-20T09:26:46Z","ec_funded":1,"ddc":["510"],"date_published":"2020-02-21T00:00:00Z","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s10955-020-02500-8","article_type":"original","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"_id":"7508","status":"public","oa_version":"Published Version","day":"21","arxiv":1,"isi":1,"year":"2020","citation":{"ama":"Bossmann L, Pavlović N, Pickl P, Soffer A. Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. 2020;178:1362-1396. doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>","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.","apa":"Bossmann, L., Pavlović, N., Pickl, P., &#38; Soffer, A. (2020). Higher order corrections to the mean-field description of the dynamics of interacting bosons. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>","ieee":"L. Bossmann, N. Pavlović, P. Pickl, and A. Soffer, “Higher order corrections to the mean-field description of the dynamics of interacting bosons,” <i>Journal of Statistical Physics</i>, vol. 178. Springer Nature, pp. 1362–1396, 2020.","chicago":"Bossmann, Lea, Nataša Pavlović, Peter Pickl, and Avy Soffer. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02500-8\">https://doi.org/10.1007/s10955-020-02500-8</a>.","short":"L. Bossmann, N. Pavlović, P. Pickl, A. Soffer, Journal of Statistical Physics 178 (2020) 1362–1396.","mla":"Bossmann, Lea, et al. “Higher Order Corrections to the Mean-Field Description of the Dynamics of Interacting Bosons.” <i>Journal of Statistical Physics</i>, vol. 178, Springer Nature, 2020, pp. 1362–96, doi:<a href=\"https://doi.org/10.1007/s10955-020-02500-8\">10.1007/s10955-020-02500-8</a>."},"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.","publisher":"Springer Nature","external_id":{"isi":["000516342200001"],"arxiv":["1905.06164"]},"file":[{"success":1,"file_id":"8780","date_created":"2020-11-20T09:26:46Z","file_size":576726,"file_name":"2020_JournStatPhysics_Bossmann.pdf","checksum":"643e230bf147e64d9cdb3f6cc573679d","access_level":"open_access","relation":"main_file","creator":"dernst","content_type":"application/pdf","date_updated":"2020-11-20T09:26:46Z"}],"intvolume":"       178"},{"month":"02","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"},{"_id":"GradSch"}],"page":"148","related_material":{"record":[{"status":"public","id":"7524","relation":"part_of_dissertation"}]},"project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"degree_awarded":"PhD","article_processing_charge":"No","date_created":"2020-02-24T09:17:27Z","author":[{"first_name":"Simon","last_name":"Mayer","id":"30C4630A-F248-11E8-B48F-1D18A9856A87","full_name":"Mayer, Simon"}],"corr_author":"1","type":"dissertation","doi":"10.15479/AT:ISTA:7514","title":"The free energy of a dilute two-dimensional Bose gas","oa":1,"publication_identifier":{"issn":["2663-337X"]},"publisher":"Institute of Science and Technology Austria","citation":{"chicago":"Mayer, Simon. “The Free Energy of a Dilute Two-Dimensional Bose Gas.” Institute of Science and Technology Austria, 2020. <a href=\"https://doi.org/10.15479/AT:ISTA:7514\">https://doi.org/10.15479/AT:ISTA:7514</a>.","mla":"Mayer, Simon. <i>The Free Energy of a Dilute Two-Dimensional Bose Gas</i>. Institute of Science and Technology Austria, 2020, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7514\">10.15479/AT:ISTA:7514</a>.","short":"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.","ama":"Mayer S. The free energy of a dilute two-dimensional Bose gas. 2020. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:7514\">10.15479/AT:ISTA:7514</a>","ieee":"S. Mayer, “The free energy of a dilute two-dimensional Bose gas,” Institute of Science and Technology Austria, 2020.","apa":"Mayer, S. (2020). <i>The free energy of a dilute two-dimensional Bose gas</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:7514\">https://doi.org/10.15479/AT:ISTA:7514</a>"},"year":"2020","supervisor":[{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"day":"24","oa_version":"Published Version","_id":"7514","status":"public","file":[{"date_created":"2020-02-24T09:15:06Z","file_size":1563429,"file_name":"thesis.pdf","file_id":"7515","creator":"dernst","date_updated":"2020-07-14T12:47:59Z","content_type":"application/pdf","access_level":"open_access","checksum":"b4de7579ddc1dbdd44ff3f17c48395f6","relation":"main_file"},{"file_id":"7516","file_name":"thesis_source.zip","date_created":"2020-02-24T09:15:16Z","file_size":2028038,"checksum":"ad7425867b52d7d9e72296e87bc9cb67","access_level":"closed","relation":"source_file","date_updated":"2020-07-14T12:47:59Z","content_type":"application/x-zip-compressed","creator":"dernst"}],"file_date_updated":"2020-07-14T12:47:59Z","ec_funded":1,"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."}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_updated":"2026-04-08T07:25:40Z","alternative_title":["ISTA Thesis"],"OA_place":"publisher","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"fulldoi":"https://doi.org/10.15479/AT:ISTA:7514","has_accepted_license":"1","date_published":"2020-02-24T00:00:00Z","ddc":["510"]},{"year":"2020","citation":{"ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “The excitation spectrum of Bose gases interacting through singular potentials,” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7. EMS Press, pp. 2331–2403, 2020.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>","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.","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. The excitation spectrum of Bose gases interacting through singular potentials. <i>Journal of the European Mathematical Society</i>. 2020;22(7):2331-2403. doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>","mla":"Boccato, Chiara, et al. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>, vol. 22, no. 7, EMS Press, 2020, pp. 2331–403, doi:<a href=\"https://doi.org/10.4171/JEMS/966\">10.4171/JEMS/966</a>.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Journal of the European Mathematical Society 22 (2020) 2331–2403.","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “The Excitation Spectrum of Bose Gases Interacting through Singular Potentials.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/JEMS/966\">https://doi.org/10.4171/JEMS/966</a>."},"publisher":"EMS Press","arxiv":1,"day":"01","das_tickbox":"1","isi":1,"oa_version":"Preprint","status":"public","_id":"8042","intvolume":"        22","external_id":{"arxiv":["1704.04819"],"isi":["000548174700006"]},"issue":"7","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-07-06T11:53:41Z","article_type":"original","fulldoi":"https://doi.org/10.4171/JEMS/966","date_published":"2020-07-01T00:00:00Z","month":"07","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"volume":22,"publication_status":"published","page":"2331-2403","quality_controlled":"1","date_created":"2020-06-29T07:59:35Z","article_processing_charge":"No","author":[{"first_name":"Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87","last_name":"Boccato","full_name":"Boccato, Chiara"},{"full_name":"Brennecke, Christian","last_name":"Brennecke","first_name":"Christian"},{"first_name":"Serena","last_name":"Cenatiempo","full_name":"Cenatiempo, Serena"},{"last_name":"Schlein","full_name":"Schlein, Benjamin","first_name":"Benjamin"}],"publication":"Journal of the European Mathematical Society","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1704.04819","open_access":"1"}],"doi":"10.4171/JEMS/966","type":"journal_article","publication_identifier":{"issn":["1435-9855"]},"oa":1,"title":"The excitation spectrum of Bose gases interacting through singular potentials"},{"publication":"Oberwolfach Reports","author":[{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521"},{"full_name":"Warzel, Simone","last_name":"Warzel","first_name":"Simone"}],"publication_identifier":{"issn":["1660-8933"]},"title":"Many-body quantum systems","doi":"10.4171/owr/2019/41","type":"journal_article","page":"2541-2603","volume":16,"department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"publication_status":"published","month":"09","date_created":"2024-03-04T11:46:12Z","article_processing_charge":"No","quality_controlled":"1","date_updated":"2026-07-06T11:53:09Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.","lang":"eng"}],"date_published":"2020-09-10T00:00:00Z","fulldoi":"https://doi.org/10.4171/owr/2019/41","article_type":"original","status":"public","_id":"15072","oa_version":"None","day":"10","das_tickbox":"1","citation":{"ista":"Hainzl C, Schlein B, Seiringer R, Warzel S. 2020. Many-body quantum systems. Oberwolfach Reports. 16(3), 2541–2603.","ama":"Hainzl C, Schlein B, Seiringer R, Warzel S. Many-body quantum systems. <i>Oberwolfach Reports</i>. 2020;16(3):2541-2603. doi:<a href=\"https://doi.org/10.4171/owr/2019/41\">10.4171/owr/2019/41</a>","ieee":"C. Hainzl, B. Schlein, R. Seiringer, and S. Warzel, “Many-body quantum systems,” <i>Oberwolfach Reports</i>, vol. 16, no. 3. EMS Press, pp. 2541–2603, 2020.","apa":"Hainzl, C., Schlein, B., Seiringer, R., &#38; Warzel, S. (2020). Many-body quantum systems. <i>Oberwolfach Reports</i>. EMS Press. <a href=\"https://doi.org/10.4171/owr/2019/41\">https://doi.org/10.4171/owr/2019/41</a>","chicago":"Hainzl, Christian, Benjamin Schlein, Robert Seiringer, and Simone Warzel. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/owr/2019/41\">https://doi.org/10.4171/owr/2019/41</a>.","mla":"Hainzl, Christian, et al. “Many-Body Quantum Systems.” <i>Oberwolfach Reports</i>, vol. 16, no. 3, EMS Press, 2020, pp. 2541–603, doi:<a href=\"https://doi.org/10.4171/owr/2019/41\">10.4171/owr/2019/41</a>.","short":"C. Hainzl, B. Schlein, R. Seiringer, S. Warzel, Oberwolfach Reports 16 (2020) 2541–2603."},"year":"2020","publisher":"EMS Press","issue":"3","intvolume":"        16"}]