[{"oa_version":"Preprint","abstract":[{"text":"We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions.","lang":"eng"}],"month":"09","intvolume":" 281","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.00992"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication_status":"published","volume":281,"issue":"6","ec_funded":1,"_id":"9462","status":"public","article_type":"original","type":"journal_article","date_updated":"2023-08-08T13:56:27Z","department":[{"_id":"RoSe"}],"acknowledgement":"Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.","publisher":"Elsevier","quality_controlled":"1","oa":1,"day":"15","publication":"Journal of Functional Analysis","isi":1,"year":"2021","doi":"10.1016/j.jfa.2021.109096","date_published":"2021-09-15T00:00:00Z","date_created":"2021-06-06T22:01:28Z","article_number":"109096","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Deuchert, A., & Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109096","ama":"Deuchert A, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 2021;281(6). doi:10.1016/j.jfa.2021.109096","short":"A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021).","ieee":"A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons,” Journal of Functional Analysis, vol. 281, no. 6. Elsevier, 2021.","mla":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis, vol. 281, no. 6, 109096, Elsevier, 2021, doi:10.1016/j.jfa.2021.109096.","ista":"Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096.","chicago":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109096."},"title":"Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons","author":[{"first_name":"Andreas","last_name":"Deuchert","full_name":"Deuchert, Andreas"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"external_id":{"arxiv":["2009.00992"],"isi":["000656508600008"]},"article_processing_charge":"No"},{"issue":"8","volume":62,"language":[{"iso":"eng"}],"file":[{"creator":"cziletti","file_size":4352640,"date_updated":"2021-10-27T12:57:06Z","file_name":"2021_JMathPhy_Lauritsen.pdf","date_created":"2021-10-27T12:57:06Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"10188","checksum":"d035be2b894c4d50d90ac5ce252e27cd"}],"publication_status":"published","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"intvolume":" 62","month":"08","scopus_import":"1","oa_version":"Published Version","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","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"ddc":["530"],"date_updated":"2023-08-11T10:29:48Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"9891","date_created":"2021-08-12T07:08:36Z","doi":"10.1063/5.0053494","date_published":"2021-08-01T00:00:00Z","publication":"Journal of Mathematical Physics","day":"01","year":"2021","has_accepted_license":"1","isi":1,"oa":1,"publisher":"AIP Publishing","quality_controlled":"1","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.","title":"Floating Wigner crystal and periodic jellium configurations","external_id":{"arxiv":["2103.07975"],"isi":["000683960800003"]},"article_processing_charge":"No","author":[{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics, vol. 62, no. 8, 083305, AIP Publishing, 2021, doi:10.1063/5.0053494.","ieee":"A. B. Lauritsen, “Floating Wigner crystal and periodic jellium configurations,” Journal of Mathematical Physics, vol. 62, no. 8. AIP Publishing, 2021.","short":"A.B. Lauritsen, Journal of Mathematical Physics 62 (2021).","apa":"Lauritsen, A. B. (2021). Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0053494","ama":"Lauritsen AB. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 2021;62(8). doi:10.1063/5.0053494","chicago":"Lauritsen, Asbjørn Bækgaard. “Floating Wigner Crystal and Periodic Jellium Configurations.” Journal of Mathematical Physics. AIP Publishing, 2021. https://doi.org/10.1063/5.0053494.","ista":"Lauritsen AB. 2021. Floating Wigner crystal and periodic jellium configurations. Journal of Mathematical Physics. 62(8), 083305."},"article_number":"083305"},{"abstract":[{"lang":"eng","text":"We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the translational symmetry (and its breaking in the Pekar approximation) makes the analysis substantially more challenging."}],"oa_version":"Published Version","scopus_import":"1","month":"10","intvolume":" 242","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"publication_status":"published","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"672e9c21b20f1a50854b7c821edbb92f","file_id":"10544","creator":"alisjak","file_size":990529,"date_updated":"2021-12-14T08:35:42Z","file_name":"2021_Springer_Feliciangeli.pdf","date_created":"2021-12-14T08:35:42Z"}],"language":[{"iso":"eng"}],"issue":"3","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"9787"}]},"volume":242,"ec_funded":1,"_id":"10224","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-14T10:32:19Z","ddc":["530"],"department":[{"_id":"RoSe"}],"file_date_updated":"2021-12-14T08:35:42Z","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is gratefully acknowledged. We would also like to thank Rupert Frank for many helpful discussions, especially related to the Gross coordinate transformation defined in Def. 4.7.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","quality_controlled":"1","oa":1,"isi":1,"has_accepted_license":"1","year":"2021","day":"25","publication":"Archive for Rational Mechanics and Analysis","page":"1835–1906","date_published":"2021-10-25T00:00:00Z","doi":"10.1007/s00205-021-01715-7","date_created":"2021-11-07T23:01:26Z","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"citation":{"chicago":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01715-7.","ista":"Feliciangeli D, Seiringer R. 2021. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 242(3), 1835–1906.","mla":"Feliciangeli, Dario, and Robert Seiringer. “The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics.” Archive for Rational Mechanics and Analysis, vol. 242, no. 3, Springer Nature, 2021, pp. 1835–1906, doi:10.1007/s00205-021-01715-7.","short":"D. Feliciangeli, R. Seiringer, Archive for Rational Mechanics and Analysis 242 (2021) 1835–1906.","ieee":"D. Feliciangeli and R. Seiringer, “The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics,” Archive for Rational Mechanics and Analysis, vol. 242, no. 3. Springer Nature, pp. 1835–1906, 2021.","ama":"Feliciangeli D, Seiringer R. The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. 2021;242(3):1835–1906. doi:10.1007/s00205-021-01715-7","apa":"Feliciangeli, D., & Seiringer, R. (2021). The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01715-7"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["2101.12566"],"isi":["000710850600001"]},"article_processing_charge":"Yes (via OA deal)","title":"The strongly coupled polaron on the torus: Quantum corrections to the Pekar asymptotics"},{"date_published":"2021-12-02T00:00:00Z","doi":"10.1007/s00023-021-01136-y","date_created":"2021-12-12T23:01:28Z","day":"02","publication":"Annales Henri Poincaré","isi":1,"year":"2021","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"NB was supported by Gruppo Nazionale per la Fisica Matematica (GNFM). RS was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 694227). PTN was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC StG MaMBoQ, Grant Agreement No. 802901). BS was supported by the NCCR SwissMAP, the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates,” and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program through the ERC-AdG CLaQS (Grant Agreement No. 834782).","title":"Bosonization of fermionic many-body dynamics","author":[{"last_name":"Benedikter","orcid":"0000-0002-1071-6091","full_name":"Benedikter, Niels P","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","first_name":"Niels P"},{"last_name":"Nam","full_name":"Nam, Phan Thành","first_name":"Phan Thành"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"last_name":"Schlein","full_name":"Schlein, Benjamin","first_name":"Benjamin"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"external_id":{"isi":["000725405700001"],"arxiv":["2103.08224"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Bosonization of Fermionic Many-Body Dynamics.” Annales Henri Poincaré. Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01136-y.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré.","mla":"Benedikter, Niels P., et al. “Bosonization of Fermionic Many-Body Dynamics.” Annales Henri Poincaré, Springer Nature, 2021, doi:10.1007/s00023-021-01136-y.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Bosonization of fermionic many-body dynamics,” Annales Henri Poincaré. Springer Nature, 2021.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Annales Henri Poincaré (2021).","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. 2021. doi:10.1007/s00023-021-01136-y","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2021). Bosonization of fermionic many-body dynamics. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-021-01136-y"},"project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"}],"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"]},"publication_status":"published","month":"12","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2103.08224","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the coupled semiclassical and mean-field scaling regime. We study a class of initial data describing collective particle–hole pair excitations on the Fermi ball. Using a rigorous version of approximate bosonization, we prove that the many-body evolution can be approximated in Fock space norm by a quasi-free bosonic evolution of the collective particle–hole excitations."}],"department":[{"_id":"RoSe"}],"date_updated":"2023-08-17T06:19:14Z","status":"public","type":"journal_article","article_type":"original","_id":"10537"},{"acknowledgement":"We thank Christian Hainzl for helpful discussions and a referee for very careful reading of the paper and many helpful suggestions. NB and RS were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694227). Part of the research of NB was conducted on the RZD18 Nice–Milan–Vienna–Moscow. NB thanks Elliott H. Lieb and Peter Otte for explanations about the Luttinger model. PTN has received funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (EXC-2111-390814868). MP acknowledges financial support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC StG MaMBoQ, grant agreement No. 802901). BS gratefully acknowledges financial support from the NCCR SwissMAP, from the Swiss National Science Foundation through the Grant “Dynamical and energetic properties of Bose-Einstein condensates” and from the European Research Council through the ERC-AdG CLaQS (grant agreement No. 834782). All authors acknowledge support for workshop participation from Mathematisches Forschungsinstitut Oberwolfach (Leibniz Association). NB, PTN, BS, and RS acknowledge support for workshop participation from Fondation des Treilles.","quality_controlled":"1","publisher":"Springer","oa":1,"isi":1,"has_accepted_license":"1","year":"2021","day":"03","publication":"Inventiones Mathematicae","page":"885-979","doi":"10.1007/s00222-021-01041-5","date_published":"2021-05-03T00:00:00Z","date_created":"2020-05-28T16:48:20Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Correlation Energy of a Weakly Interacting Fermi Gas.” Inventiones Mathematicae. Springer, 2021. https://doi.org/10.1007/s00222-021-01041-5.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2021. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 225, 885–979.","mla":"Benedikter, Niels P., et al. “Correlation Energy of a Weakly Interacting Fermi Gas.” Inventiones Mathematicae, vol. 225, Springer, 2021, pp. 885–979, doi:10.1007/s00222-021-01041-5.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Correlation energy of a weakly interacting Fermi gas,” Inventiones Mathematicae, vol. 225. Springer, pp. 885–979, 2021.","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Inventiones Mathematicae 225 (2021) 885–979.","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. 2021;225:885-979. doi:10.1007/s00222-021-01041-5","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., & Seiringer, R. (2021). Correlation energy of a weakly interacting Fermi gas. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-021-01041-5"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","first_name":"Niels P","full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","last_name":"Benedikter"},{"first_name":"Phan Thành","last_name":"Nam","full_name":"Nam, Phan Thành"},{"full_name":"Porta, Marcello","last_name":"Porta","first_name":"Marcello"},{"first_name":"Benjamin","last_name":"Schlein","full_name":"Schlein, Benjamin"},{"orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000646573600001"],"arxiv":["2005.08933"]},"title":"Correlation energy of a weakly interacting Fermi gas","abstract":[{"lang":"eng","text":"We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy."}],"oa_version":"Published Version","scopus_import":"1","month":"05","intvolume":" 225","publication_identifier":{"issn":["0020-9910"],"eissn":["1432-1297"]},"publication_status":"published","file":[{"date_created":"2022-05-16T12:23:40Z","file_name":"2021_InventMath_Benedikter.pdf","date_updated":"2022-05-16T12:23:40Z","file_size":1089319,"creator":"dernst","file_id":"11386","checksum":"f38c79dfd828cdc7f49a34b37b83d376","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"volume":225,"ec_funded":1,"_id":"7901","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-21T06:30:30Z","ddc":["510"],"department":[{"_id":"RoSe"}],"file_date_updated":"2022-05-16T12:23:40Z"}]