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.
Highlights
Remark 1.3. — the usual description is limited to the physical dimension d = 3, here we explored other dimensions in the hope to shed some light on the problems which are still open
Since the functionals appearing in Theorems 1.1 and 1.2 above are all expressed as minimal values, the natural tool to deal with their convergence is the Γ-convergence which we shortly introduce
Multimarginal optimal transportation and composition of optimal transport plans. — In this subsection we present some basic results about multimarginal optimal transportation with Coulomb cost
Summary
Abstract. — We present some progress in the direction of determining the semiclassical limit of the Levy-Lieb or Hohenberg-Kohn universal functional in density functional theory for Coulomb systems. — We present some progress in the direction of determining the semiclassical limit of the Levy-Lieb or Hohenberg-Kohn universal functional in density functional theory for Coulomb systems. Résumé (Transport optimal avec coût coulombien et limite semi-classique de la théorie de la fonctionnelle de la densité). Nous présentons des progrès récents en vue de la détermination de la limite semi-classique de la fonctionnelle universelle de Levy-Lieb ou Hohenberg-Kohn en théorie de la fonctionnelle de la densité pour des systèmes coulombiens. Nous donnons en particulier une preuve du fait que, pour des systèmes de bosons avec un nombre arbitraire de particules, la limite est le problème de transport optimal multi-marginal à coût coulombien, de même que pour les systèmes de fermions à deux ou trois particules. Nous nous appuyons sur certaines techniques de la théorie du transport optimal
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
