Free Energies of Dilute Bose gases: upper bound

Details Free Energies of Dilute Bose gases: upper bound Free Energies of Dilute Bose gases: upper bound

2009-06-07

arxiv.org/abs/0906.1322v2

J. STAT. PHYS Volume 141, Number 4, 683-726 2010 Volume 141, Number 4, 683-726,

Physics

Mathematical Physics

56 pages, no figures

Scientific paper

We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e., when $a^3\rho\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$ the free energy difference per volume between interacting and ideal Bose gases is equal to $4\pi a (2\rho^2-[\rho-\rhoc]^2_+)$. Here, $\rhoc(T)$ denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot ]_+$ $=$ $\max\{\cdot, 0\}$ denotes the positive part.

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