Calculus of Variations and Geometric Measure Theory

G. Buttazzo - L. De Pascale - P. Gori-Giorgi

Optimal-transport formulation of electronic density-functional theory

created by depascal on 23 May 2012


Accepted Paper

Inserted: 23 may 2012
Last Updated: 23 may 2012

Journal: Physical Review A
Pages: 12
Year: 2012


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 $\rho(r)$ 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.