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 ρ(r) is equivalent to find the optimal way of transporting N − 1 times the density ρ 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.
Optimal-transport formulation of electronic density-functional theory / Buttazzo G; De Pascale L.; Gori-Giorgi P.. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - STAMPA. - 85:6(2012), pp. 1-11. [10.1103/PhysRevA.85.062502]
Optimal-transport formulation of electronic density-functional theory
DE PASCALE, LUIGI;
2012
Abstract
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 ρ(r) is equivalent to find the optimal way of transporting N − 1 times the density ρ 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.File | Dimensione | Formato | |
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