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arXiv · 2405.03378

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

Florian Haberberger·Christian Hainzl·Benjamin Schlein·Arnaud Triay
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Abstract

We consider a Bose gas at density $\rho > 0$, interacting through a repulsive potential $V \in L^2 (\mathbb{R}^3)$ with scattering length $\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \lesssim \rho \mathfrak{a}$. Combined with the recent lower bound obtained in \cite{HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order $\mathfrak{a} \rho^2 (\rho \mathfrak{a}^3)^{1/2}$.

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Florian Haberberger, Christian Hainzl, Benjamin Schlein, Arnaud Triay. 2024-05-06. Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature. https://arxiv.org/abs/2405.03378

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