{"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.","quality_controlled":"1","language":[{"iso":"eng"}],"publication_status":"published","month":"03","publisher":"Springer Nature","license":"https://creativecommons.org/licenses/by/4.0/","has_accepted_license":"1","page":"1217-1271","date_created":"2020-04-08T15:18:03Z","title":"Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature","ddc":["510"],"file":[{"date_updated":"2020-11-20T13:17:42Z","date_created":"2020-11-20T13:17:42Z","access_level":"open_access","content_type":"application/pdf","file_size":704633,"file_id":"8785","success":1,"creator":"dernst","file_name":"2020_ArchRatMechanicsAnalysis_Deuchert.pdf","checksum":"b645fb64bfe95bbc05b3eea374109a9c","relation":"main_file"}],"year":"2020","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2020-11-20T13:17:42Z","project":[{"grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"ec_funded":1,"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>","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>.","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.","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.","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>.","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>"},"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Deuchert, Andreas","first_name":"Andreas","last_name":"Deuchert","id":"4DA65CD0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3146-6746"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"intvolume":"       236","oa":1,"issue":"6","date_published":"2020-03-09T00:00:00Z","abstract":[{"lang":"eng","text":"We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Bose–Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution."}],"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"date_updated":"2023-09-05T14:18:49Z","doi":"10.1007/s00205-020-01489-4","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"RoSe"}],"volume":236,"article_type":"original","status":"public","publication":"Archive for Rational Mechanics and Analysis","external_id":{"arxiv":["1901.11363"],"isi":["000519415000001"]},"_id":"7650","type":"journal_article","scopus_import":"1","isi":1,"day":"09"}