标题： 零温下大费米系统的定量半经典极限 显示英文标题

标题： The quantitative semi-classical limit of a large Fermi system at zero temperature

摘要： 本文中我们考虑三维空间中一个大费米子系统的平均场和半经典极限的联合情形。我们研究基态的Wigner函数收敛到经典的Thomas-Fermi理论的情况。本文的主要新意在于量化了相对于半经典参数的收敛速度。其中的关键之一是最近关于Hartree理论满足的半经典交换估计有效性的最新成果。奇异势，包括库仑相互作用，也被纳入考虑范围。 显示英文摘要

摘要： In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi theory. The main novelty of the present article is quantifying the convergence rate with respect to the semi-classical parameter. One of the main ingredients is a recent result on the validity of semi-classical commutator estimates satisfied by the Hartree theory. Singular potentials, up to the Coulomb interaction, are included.