Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature

2024/05/06 by Haberberger, Florian, Hainzl, Christian, Schlein, Benjamin +1 · 2 citations
#81V73 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2405.03378

Abstract

We consider a Bose gas at density ρ> 0, interacting through a repulsive potential V ∈ L² (ℝ³) with scattering length \mathfraka > 0. We prove an upper bound for the free energy of the system, valid at low temperature T \lesssim ρ\mathfraka. Combined with the recent lower bound obtained in \citeHabHaiNamSeiTri-23, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order \mathfraka ρ² (ρ\mathfraka³)^1/2.

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