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arXiv · 2505.24706

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

Esteban Cárdenas
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Abstract

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.

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Esteban Cárdenas. 2025-05-30. The quantitative semi-classical limit of a large Fermi system at zero temperature. https://arxiv.org/abs/2505.24706

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