[Limite semi-classique de la fonctionnelle de Levy–Lieb en théorie de la fonctionnelle de densité]
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.
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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@article{CRMATH_2018__356_4_449_0,
author = {Lewin, Mathieu},
title = {Semi-classical limit of the {Levy{\textendash}Lieb} functional in {Density} {Functional} {Theory}},
journal = {Comptes Rendus. Math\'ematique},
pages = {449--455},
publisher = {Elsevier},
volume = {356},
number = {4},
year = {2018},
doi = {10.1016/j.crma.2018.03.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.03.002/}
}
TY - JOUR AU - Lewin, Mathieu TI - Semi-classical limit of the Levy–Lieb functional in Density Functional Theory JO - Comptes Rendus. Mathématique PY - 2018 SP - 449 EP - 455 VL - 356 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.03.002/ DO - 10.1016/j.crma.2018.03.002 LA - en ID - CRMATH_2018__356_4_449_0 ER -
%0 Journal Article %A Lewin, Mathieu %T Semi-classical limit of the Levy–Lieb functional in Density Functional Theory %J Comptes Rendus. Mathématique %D 2018 %P 449-455 %V 356 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.03.002/ %R 10.1016/j.crma.2018.03.002 %G en %F CRMATH_2018__356_4_449_0
Lewin, Mathieu. Semi-classical limit of the Levy–Lieb functional in Density Functional Theory. Comptes Rendus. Mathématique, Tome 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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