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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
Mots clés: Gaz uniforme d’électrons, théorie de la fonctionnelle de la densité, limite thermodynamique, mécanique statistique, limites de champ moyen, transport optimal

Résumé - Abstract

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.


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