标题： 稀释玻色气体在低温下的自由能上界 显示英文标题

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

摘要： 我们考虑一个密度为$\rho > 0$的玻色气体，通过排斥势$V \in L^2 (\mathbb{R}^3)$相互作用，散射长度为$\mathfrak{a} > 0$。 我们证明了系统自由能的上界，在低温$T \lesssim \rho \mathfrak{a}$下有效。 结合最近在\cite{HabHaiNamSeiTri-23}中得到的下界，我们的估计解决了单位体积的自由能，直到包括 Lee--Huang--Yang 阶次$\mathfrak{a} \rho^2 (\rho \mathfrak{a}^3)^{1/2}$。 显示英文摘要

摘要： 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 $\mathfrak{a} \rho^2 (\rho \mathfrak{a}^3)^{1/2}$.