{"_id":"554","author":[{"first_name":"Marcin M","full_name":"Napiórkowski, Marcin M","last_name":"Napiórkowski","id":"4197AD04-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Robin","full_name":"Reuvers, Robin","last_name":"Reuvers"},{"first_name":"Jan","full_name":"Solovej, Jan","last_name":"Solovej"}],"doi":"10.1007/s00220-017-3064-x","abstract":[{"lang":"eng","text":"We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.)."}],"publication":"Communications in Mathematical Physics","publication_status":"published","type":"journal_article","date_updated":"2021-01-12T08:02:35Z","volume":360,"publication_identifier":{"issn":["00103616"]},"external_id":{"arxiv":["1511.05953"]},"project":[{"grant_number":"P27533_N27","_id":"25C878CE-B435-11E9-9278-68D0E5697425","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","call_identifier":"FWF"}],"status":"public","page":"347-403","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"month":"05","date_created":"2018-12-11T11:47:09Z","citation":{"mla":"Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical Physics</i>, vol. 360, no. 1, Springer, 2018, pp. 347–403, doi:<a href=\"https://doi.org/10.1007/s00220-017-3064-x\">10.1007/s00220-017-3064-x</a>.","ama":"Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional II: The dilute Limit. <i>Communications in Mathematical Physics</i>. 2018;360(1):347-403. doi:<a href=\"https://doi.org/10.1007/s00220-017-3064-x\">10.1007/s00220-017-3064-x</a>","short":"M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403.","ieee":"M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy functional II: The dilute Limit,” <i>Communications in Mathematical Physics</i>, vol. 360, no. 1. Springer, pp. 347–403, 2018.","chicago":"Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical Physics</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00220-017-3064-x\">https://doi.org/10.1007/s00220-017-3064-x</a>.","ista":"Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.","apa":"Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. (2018). The Bogoliubov free energy functional II: The dilute Limit. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-017-3064-x\">https://doi.org/10.1007/s00220-017-3064-x</a>"},"quality_controlled":"1","scopus_import":1,"title":"The Bogoliubov free energy functional II: The dilute Limit","main_file_link":[{"url":"https://arxiv.org/abs/1511.05953","open_access":"1"}],"oa_version":"Submitted Version","issue":"1","publist_id":"7260","language":[{"iso":"eng"}],"intvolume":"       360","day":"01","publisher":"Springer","year":"2018","date_published":"2018-05-01T00:00:00Z"}