[{"publication_status":"published","publist_id":"4551","year":"2008","date_published":"2008-05-01T00:00:00Z","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0608069","open_access":"1"}],"_id":"2374","extern":1,"month":"05","quality_controlled":0,"day":"01","intvolume":" 279","date_created":"2018-12-11T11:57:17Z","page":"595 - 636","citation":{"apa":"Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. *Communications in Mathematical Physics*, *279*(3), 595–636. https://doi.org/10.1007/s00220-008-0428-2","short":"R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636.","ieee":"R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” *Communications in Mathematical Physics*, vol. 279, no. 3, pp. 595–636, 2008.","ama":"Seiringer R. Free energy of a dilute Bose gas: Lower bound. *Communications in Mathematical Physics*. 2008;279(3):595-636. doi:10.1007/s00220-008-0428-2","mla":"Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” *Communications in Mathematical Physics*, vol. 279, no. 3, Springer, 2008, pp. 595–636, doi:10.1007/s00220-008-0428-2.","chicago":"Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” *Communications in Mathematical Physics* 279, no. 3 (2008): 595–636. https://doi.org/10.1007/s00220-008-0428-2.","ista":"Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications in Mathematical Physics. 279(3), 595–636."},"doi":"10.1007/s00220-008-0428-2","status":"public","author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer"}],"issue":"3","volume":279,"date_updated":"2019-04-26T07:22:11Z","abstract":[{"text":"A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density Q and temperature T. In the dilute regime, i.e., when a3 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2}-[ - c]2+). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ · ]+ = max{ ·, 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ~ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one.","lang":"eng"}],"publication":"Communications in Mathematical Physics","oa":1,"type":"journal_article","publisher":"Springer","title":"Free energy of a dilute Bose gas: Lower bound"}]