Mathematical physics/Calculus of variations
Semi-classical limit of the Levy–Lieb functional in Density Functional Theory
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 449-455.

In a recent work, Bindini and De Pascale have introduced a regularization of N-particle symmetric probabilities that 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.

Dans un travail récent, Bindini et de Pascale ont introduit une régularisation des probabilités symétriques décrivant N particules indiscernables, qui préserve la densité à une particule. Nous étendons ici leur construction aux états quantiques mixtes de fermions. Ceci nous permet de démontrer la convergence de la fonctionnelle de Levy–Lieb, objet central de la théorie de la fonctionnelle de densité (DFT), vers le transport optimal multi-marges associé, à la limite semi-classique. Notre résultat est valable pour les états mixtes de n'importe quel nombre de particules N, avec ou sans spin.

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DOI: 10.1016/j.crma.2018.03.002
Lewin, Mathieu 1

1 CNRS & CEREMADE, Université Paris-Dauphine, PSL Research University, 75016 Paris, France
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Lewin, Mathieu. Semi-classical limit of the Levy–Lieb functional in Density Functional Theory. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 449-455. doi : 10.1016/j.crma.2018.03.002. http://www.numdam.org/articles/10.1016/j.crma.2018.03.002/

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