Statistical Mechanics of the Uniform Electron Gas

Mathieu Lewin (1) , Elliott H. Lieb (2) , Robert Seiringer (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Departments of Physics and Mathematics
3 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

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.

Domaines: Physique mathématique [math-ph]

Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. Statistical Mechanics of the Uniform Electron Gas. Journal de l'École polytechnique — Mathématiques, 2018, 5, pp.79-116. ⟨10.5802/jep.64⟩. ⟨hal-01534112⟩