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

Mathieu Lewin (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Chimie-Physique [physics.chem-ph]

Mathieu Lewin. Semi-classical limit of the Levy-Lieb functional in Density Functional Theory. Comptes Rendus. Mathématique, 2018, 356 (4), pp.449-455. ⟨10.1016/j.crma.2018.03.002⟩. ⟨hal-01534079v4⟩