10.1007/s00220-008-0428-2
Robert Seiringer
Robert
Seiringer
Free energy of a dilute Bose gas: Lower bound
Springer
2008
2018-12-11T11:57:17Z
2019-04-26T07:22:11Z
journal_article
https://research-explorer.app.ist.ac.at/record/2374
https://research-explorer.app.ist.ac.at/record/2374.json
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.