{"status":"public","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.","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.00992"}],"volume":281,"citation":{"mla":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>, vol. 281, no. 6, 109096, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>.","ista":"Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 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,” <i>Journal of Functional Analysis</i>, vol. 281, no. 6. Elsevier, 2021.","apa":"Deuchert, A., &#38; Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>","ama":"Deuchert A, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. 2021;281(6). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>","chicago":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>."},"publication":"Journal of Functional Analysis","month":"09","isi":1,"publication_status":"published","quality_controlled":"1","doi":"10.1016/j.jfa.2021.109096","_id":"9462","year":"2021","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Deuchert","first_name":"Andreas","full_name":"Deuchert, Andreas"},{"full_name":"Seiringer, Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"external_id":{"arxiv":["2009.00992"],"isi":["000656508600008"]},"date_updated":"2023-08-08T13:56:27Z","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"}],"ec_funded":1,"oa":1,"date_published":"2021-09-15T00:00:00Z","oa_version":"Preprint","department":[{"_id":"RoSe"}],"article_number":"109096","publisher":"Elsevier","article_type":"original","type":"journal_article","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","call_identifier":"H2020"}],"intvolume":"       281","issue":"6","day":"15","title":"Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons","article_processing_charge":"No","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"language":[{"iso":"eng"}],"date_created":"2021-06-06T22:01:28Z"}