Free Energies of Dilute Bose gases: upper bound

Abstract

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 $4πa (2ρ^2-[ρ-\rhoc]^2_+)$. Here, $\rhoc(T)$ denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot {]}_{+}$ $=$ $\max \{\cdot ,0\}$ denotes the positive part.

56 pages, no figures

References in corpus (5)

• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• Free Energy of a Dilute Bose Gas: Lower Bound
• The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length
• A Lower Bound on the Ground State Energy of Dilute Bose Gas

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