[Mécanique statistique pour le gaz uniforme d’électrons]
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.
Accepté le :
Publié le :
DOI : 10.5802/jep.64
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
CC-BY-ND 4.0
@article{JEP_2018__5__79_0,
author = {Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
title = {Statistical mechanics of the~uniform~electron~gas},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {79--116},
publisher = {\'Ecole polytechnique},
volume = {5},
year = {2018},
doi = {10.5802/jep.64},
zbl = {06988574},
mrnumber = {3732693},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.64/}
}
TY - JOUR AU - Mathieu Lewin AU - Elliott H. Lieb AU - Robert Seiringer TI - Statistical mechanics of the uniform electron gas JO - Journal de l’École polytechnique — Mathématiques PY - 2018 SP - 79 EP - 116 VL - 5 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.64/ DO - 10.5802/jep.64 LA - en ID - JEP_2018__5__79_0 ER -
%0 Journal Article %A Mathieu Lewin %A Elliott H. Lieb %A Robert Seiringer %T Statistical mechanics of the uniform electron gas %J Journal de l’École polytechnique — Mathématiques %D 2018 %P 79-116 %V 5 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.64/ %R 10.5802/jep.64 %G en %F JEP_2018__5__79_0
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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