The semi-classical limit of large fermionic systems

Fournais, Søren; Lewin, Mathieu; Solovej, Jan Philip

Fournais, Søren; Lewin, Mathieu; Solovej, Jan Philip (2018), The semi-classical limit of large fermionic systems, Calculus of Variations and Partial Differential Equations, 57, 4, p. n°105. 10.1007/s00526-018-1374-2

Type

Article accepté pour publication ou publié

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https://hal.archives-ouvertes.fr/hal-01211494

Date

2018

Nom de la revue

Calculus of Variations and Partial Differential Equations

Volume

Numéro

Éditeur

Springer

Pages

n°105

Résumé (EN)

We study a system of N fermions in the regime where the intensity of the interaction scales as 1/N and with an effective semi-classical parameter ℏ=N−1/d where d is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas-Fermi minimizers in the limit N→∞. The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti-Hewitt-Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.

Mots-clés

fermions; physique mathématique