Optimal-transport formulation of electronic density-functional theory

Buttazzo, Giuseppe and Pascale, Luigi De and Gori-Giorgi, Paola (2012) Optimal-transport formulation of electronic density-functional theory. Physical review. A, Atomic, Molecular, and Optical Physics, 85 . 062502. ISSN 1094-1622

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Abstract

SUMMARY The most challenging scenario for Kohn-Sham density functional theory, that is when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well established field of mathematics and economics. In practice, we show that solving the problem of finding the minimum possible internal repulsion energy for $N$ electrons in a given density $\rho(\rv)$ is equivalent to find the optimal way of transporting $N-1$ times the density $\rho$ into itself, with cost function given by the Coulomb repulsion. We use this link to put the strong-interaction limit of density functional theory on firm grounds and to discuss the potential practical aspects of this reformulation.

Item Type: Article Imported from arXiv Area01 - Scienze matematiche e informatiche > MAT/05 - Analisi matematica Dipartimenti (from 2013) > DIPARTIMENTO DI MATEMATICA dott.ssa Sandra Faita 05 Aug 2013 12:48 05 Aug 2013 12:48 http://eprints.adm.unipi.it/id/eprint/1342

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