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Statistical mechanics of the uniform electron gas
[Mécanique statistique pour le gaz uniforme d’électrons]
Mathieu Lewin1 ; Elliott H. Lieb2 ; Robert Seiringer3
1 CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University F-75016 Paris, France
2 Departments of Mathematics and Physics, Jadwin Hall, Princeton University Washington Rd., Princeton, NJ 08544, USA
3 IST Austria (Institute of Science and Technology Austria) Am Campus 1, 3400 Klosterneuburg, Austria
Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 79-116.

Dans cet article nous définissons et étudions le gaz uniforme d’électrons, un système comprenant une infinité de particules arrangées de sorte que la densité moyenne soit constante dans tout l’espace. Ceci est en principe différent du Jellium, qui comprend une charge uniforme positive sans aucune contrainte sur la densité des électrons. Nous démontrons que le gaz uniforme d’électrons s’obtient en théorie de la fonctionnelle de la densité, dans la limite où la densité du système varie lentement. Nous construisons également le gaz uniforme quantique et montrons la convergence vers le gaz classique dans le régime de faible densité.

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.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.64
Classification : 82B03, 81V70, 49K21
Keywords: Uniform electron gas, Density Functional Theory, thermodynamic limit, statistical mechanics, mean-field limit, optimal transport
Mot clés : Gaz uniforme d’électrons, théorie de la fonctionnelle de la densité, limite thermodynamique, mécanique statistique, limites de champ moyen, transport optimal
Mathieu Lewin 1 ; Elliott H. Lieb 2 ; Robert Seiringer 3

1 CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University F-75016 Paris, France
2 Departments of Mathematics and Physics, Jadwin Hall, Princeton University Washington Rd., Princeton, NJ 08544, USA
3 IST Austria (Institute of Science and Technology Austria) Am Campus 1, 3400 Klosterneuburg, Austria
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mathieu Lewin; Elliott H. Lieb; Robert Seiringer. Statistical mechanics of the uniform electron gas. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 79-116. doi : 10.5802/jep.64. https://jep.centre-mersenne.org/articles/10.5802/jep.64/

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