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hal-00675594, version 1

Mean-field models for disordered crystals

Eric Cancès 1, 2, Salma Lahbabi (, https://www.rocq.inria.fr/micmac/spip.php?rubrique170) 1, 2, 3, Mathieu Lewin () 3

(2012)

Abstract: In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model (rHF). We consider both (short-range) Yukawa and (long-range) Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.

  • 1:  Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
  • Ecole des Ponts ParisTech
  • 2:  MICMAC (INRIA Paris - Rocquencourt)
  • Ecole des Ponts ParisTech – INRIA
  • 3:  Laboratoire d'Analyse, Géométrie et Modélisation (AGM)
  • CNRS : UMR8088 – Université de Cergy Pontoise
  • Domain : Mathematics/Mathematical Physics
  • Keywords : random Schrödinger operators – disordered crystals – electronic structure – Hartree-Fock theory – mean-field models – density functional theory – thermodynamic limit
 
  • hal-00675594, version 1
  • http://hal.archives-ouvertes.fr/hal-00675594
  • oai:hal.archives-ouvertes.fr:hal-00675594
  • From: Salma Lahbabi <>
  • Submitted on: Friday, 2 March 2012 09:04:45
  • Updated on: Tuesday, 20 March 2012 15:01:20