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Semi-classical limit of the Levy-Lieb functional in Density Functional Theory

Lewin, Mathieu (2018), Semi-classical limit of the Levy-Lieb functional in Density Functional Theory, Comptes rendus. Mathématique, 356, 4, p. 449-455. 10.1016/j.crma.2018.03.002

Type
Article accepté pour publication ou publié
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https://hal.archives-ouvertes.fr/hal-01534079
Date
2018
Nom de la revue
Comptes rendus. Mathématique
Volume
356
Numéro
4
Pages
449-455
Identifiant publication
Métadonnées
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Auteur(s)
Lewin, Mathieu cc
Résumé (EN)
In a recent work, Bindini and De Pascale have introduced a regularization of N-particle symmetric probabilities which preserves their one-particle marginals. In this short note, we extend their construction to mixed quantum fermionic states. This enables us to prove the convergence of the Levy-Lieb functional in Density Functional Theory , to the corresponding multi-marginal optimal transport in the semi-classical limit. Our result holds for mixed states of any particle number N, with or without spin.
Mots-clés
Levy-Lieb functional; Density Functional Theory