We derive an upper bound on the free energy of a Bose gas at density ρ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595-636, 2008), our result proves that in the low density limit, i.e., when a~3ρ?1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to,. Here, ρ_c(T) denotes the critical density for Bose-Einstein condensation (for the ideal Bose gas), and [·]_+=max {·,0} denotes the positive part.
展开▼
机译：我们推导了玻色气体在密度ρ和温度T下的自由能的上限。结合塞林格先前得出的下限（Commun。Math。Phys。279（3）：595-636，2008），结果证明，在低密度极限下，即当a〜3ρ？1时，其中a表示配对相互作用势的散射长度，Δf的超前项，相互作用的和理想的Bose气体之间的单位体积自由能差，等于。此处，ρ_c（T）表示Bose-Einstein凝聚的临界密度（对于理想的Bose气体），[·] _ + = max {·，0}表示正部分。
展开▼
