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

Mathieu Lewin

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

Mathematical Physics 2018-03-08 v4 Analysis of PDEs math.MP Chemical Physics

Authors: Mathieu Lewin

Abstract

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.

Keywords

Levy-Lieb functional density functional theory semi-classical limit multi-marginal optimal transport mixed quantum fermionic states N-particle symmetric probabilities

Cite

@article{arxiv.1706.02199,
  title  = {Semi-classical limit of the Levy-Lieb functional in Density Functional Theory},
  author = {Mathieu Lewin},
  journal= {arXiv preprint arXiv:1706.02199},
  year   = {2018}
}

Comments

Final version to appear in Comptes rendus de l'Acad{\'e}mie des Sciences, Math{\'e}matiques

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

Abstract

Keywords

Cite

Comments

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