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Mathieu Lewin; Elliott H. Lieb; Robert Seiringer
Statistical mechanics of the uniform electron gas
(Mécanique statistique pour le gaz uniforme d’électrons)
Journal de l'École polytechnique — Mathématiques, 5 (2018), p. 79-116, doi: 10.5802/jep.64
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Class. Math.: 82B03, 81V70, 49K21
Keywords: Uniform electron gas, Density Functional Theory, thermodynamic limit, statistical mechanics, mean-field limit, optimal transport

Résumé - Abstract

In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.

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