{"year":"2018","publisher":"Springer Nature","date_updated":"2023-09-19T14:33:12Z","department":[{"_id":"RoSe"}],"publication_status":"published","article_processing_charge":"No","page":"1037-1090","type":"journal_article","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","language":[{"iso":"eng"}],"quality_controlled":"1","project":[{"name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"oa":1,"external_id":{"isi":["000435367300003"],"arxiv":["1511.05935"]},"date_published":"2018-09-01T00:00:00Z","publication":"Archive for Rational Mechanics and Analysis","volume":229,"oa_version":"Preprint","status":"public","_id":"6002","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1511.05935","open_access":"1"}],"doi":"10.1007/s00205-018-1232-6","publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"month":"09","abstract":[{"lang":"eng","text":"The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation-invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove the existence of a phase transition in this model and provide its phase diagram."}],"intvolume":"       229","scopus_import":"1","date_created":"2019-02-14T13:40:53Z","author":[{"last_name":"Napiórkowski","full_name":"Napiórkowski, Marcin M","id":"4197AD04-F248-11E8-B48F-1D18A9856A87","first_name":"Marcin M"},{"first_name":"Robin","full_name":"Reuvers, Robin","last_name":"Reuvers"},{"full_name":"Solovej, Jan Philip","last_name":"Solovej","first_name":"Jan Philip"}],"day":"01","title":"The Bogoliubov free energy functional I: Existence of minimizers and phase diagram","issue":"3","citation":{"chicago":"Napiórkowski, Marcin M, Robin Reuvers, and Jan Philip Solovej. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00205-018-1232-6\">https://doi.org/10.1007/s00205-018-1232-6</a>.","ista":"Napiórkowski MM, Reuvers R, Solovej JP. 2018. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. Archive for Rational Mechanics and Analysis. 229(3), 1037–1090.","short":"M.M. Napiórkowski, R. Reuvers, J.P. Solovej, Archive for Rational Mechanics and Analysis 229 (2018) 1037–1090.","ama":"Napiórkowski MM, Reuvers R, Solovej JP. The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics and Analysis</i>. 2018;229(3):1037-1090. doi:<a href=\"https://doi.org/10.1007/s00205-018-1232-6\">10.1007/s00205-018-1232-6</a>","apa":"Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. P. (2018). The Bogoliubov free energy functional I: Existence of minimizers and phase diagram. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-018-1232-6\">https://doi.org/10.1007/s00205-018-1232-6</a>","ieee":"M. M. Napiórkowski, R. Reuvers, and J. P. Solovej, “The Bogoliubov free energy functional I: Existence of minimizers and phase diagram,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 229, no. 3. Springer Nature, pp. 1037–1090, 2018.","mla":"Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 229, no. 3, Springer Nature, 2018, pp. 1037–90, doi:<a href=\"https://doi.org/10.1007/s00205-018-1232-6\">10.1007/s00205-018-1232-6</a>."}}