@article{2374, abstract = {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 = {Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {3}, pages = {595 -- 636}, publisher = {Springer}, title = {{Free energy of a dilute Bose gas: Lower bound}}, doi = {10.1007/s00220-008-0428-2}, volume = {279}, year = {2008}, }