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

摘要

We present some progress in the direction of determining the semiclassicallimit of the Hoenberg-Kohn universal functional in Density Functional Theoryfor Coulomb systems. In particular we give a proof of the fact that for Bosonicsystems with an arbitrary number of particles the limit is the multimarginaloptimal transport problem with Coulomb cost and that the same holds forFermionic systems with 2 or 3 particles. Comparisons with previous results arereported . The approach is based on some techniques from the optimaltransportation theory.