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

Mathieu Lewin

doi:10.1016/j.crma.2018.03.002

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

Mathieu Lewin

Université Paris Dauphine

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Translated title of the contribution	Limite semi-classique de la fonctionnelle de Levy–Lieb en théorie de la fonctionnelle de densité
Original language	English
Pages (from-to)	449-455
Number of pages	7
Journal	Comptes Rendus Mathematique
Volume	356
Issue number	4
DOIs	https://doi.org/10.1016/j.crma.2018.03.002
Publication status	Published - 1 Apr 2018
Externally published	Yes

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10.1016/j.crma.2018.03.002

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title = "Semi-classical limit of the Levy–Lieb functional in Density Functional Theory",

abstract = "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.",

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AB - 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.

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

Abstract

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