Optimal-transport formulation of electronic density-functional theory

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

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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 to solve the problem of finding the minimum possible internal repulsion energy for N electrons in a given density ρ(r) is equivalent to find the optimal way of transporting N-1 times the density ρ into itself, with the cost function given by the Coulomb repulsion. We use this link to set the strong-interaction limit of density-functional theory on firm ground and to discuss the potential practical aspects of this reformulation. © 2012 American Physical Society.
Original languageEnglish
Article number062502
Pages (from-to)062502
Number of pages11
JournalPhysical Review A. Atomic, Molecular and Optical Physics
Publication statusPublished - 2012


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