--- _id: '2374' abstract: - lang: eng 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. author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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' apa: 'Seiringer, R. (2008). Free energy of a dilute Bose gas: Lower bound. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-008-0428-2' chicago: 'Seiringer, Robert. “Free Energy of a Dilute Bose Gas: Lower Bound.” Communications in Mathematical Physics. Springer, 2008. https://doi.org/10.1007/s00220-008-0428-2.' ieee: 'R. Seiringer, “Free energy of a dilute Bose gas: Lower bound,” Communications in Mathematical Physics, vol. 279, no. 3. Springer, pp. 595–636, 2008.' ista: 'Seiringer R. 2008. Free energy of a dilute Bose gas: Lower bound. Communications in Mathematical Physics. 279(3), 595–636.' 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.' short: R. Seiringer, Communications in Mathematical Physics 279 (2008) 595–636. date_created: 2018-12-11T11:57:17Z date_published: 2008-05-01T00:00:00Z date_updated: 2021-01-12T06:57:06Z day: '01' doi: 10.1007/s00220-008-0428-2 extern: 1 intvolume: ' 279' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0608069 month: '05' oa: 1 page: 595 - 636 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4551' quality_controlled: 0 status: public title: 'Free energy of a dilute Bose gas: Lower bound' type: journal_article volume: 279 year: '2008' ...