Optimal transport with Coulomb cost and the semiclassical limit of Density Functional Theory

Abstract

We present some progress in the direction of determining the semiclassical limit of the Hoenberg-Kohn universal functional in Density Functional Theory for Coulomb systems. In particular we give a proof of the fact that for Bosonic systems with an arbitrary number of particles the limit is the multimarginal optimal transport problem with Coulomb cost and that the same holds for Fermionic systems with 2 or 3 particles. Comparisons with previous results are reported . The approach is based on some techniques from the optimal transportation theory.

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• Density functional theory for strongly interacting electrons
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• Optimal transportation for the determinant
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Cited by in corpus (1)

• Smoothing of transport plans with fixed marginals and rigorous semiclassical limit of the Hohenberg-Kohn functional