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

@article{Bindini2017OptimalTW,
  title={Optimal transport with Coulomb cost and the semiclassical limit of Density Functional Theory},
  author={Ugo Bindini and Luigi De Pascale},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
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… 
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