Convergence of Levy-Lieb to Thomas-Fermi density functional

TL;DR

This paper proves that the Levy-Lieb density functional converges to the Thomas-Fermi functional in the semiclassical limit, providing an alternative proof of the validity of atomic Thomas-Fermi theory.

Contribution

It demonstrates the Gamma-convergence of Levy-Lieb to Thomas-Fermi functional, offering a new proof of atomic Thomas-Fermi theory's validity.

Findings

Gamma-convergence of Levy-Lieb to Thomas-Fermi functional

Simplified proof of atomic Thomas-Fermi theory validity

Clarification of the semiclassical mean-field limit

Abstract

We prove that the Levy-Lieb density functional Gamma-converges to the Thomas-Fermi functional in the semiclassical mean-field limit. In particular, this aides an easy alternative proof of the validity of the atomic Thomas-Fermi theory which was first established by Lieb and Simon.