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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2013

Mean-field models for disordered crystals

Résumé

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.
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Dates et versions

hal-00675594 , version 1 (02-03-2012)

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Eric Cancès, Salma Lahbabi, Mathieu Lewin. Mean-field models for disordered crystals. Journal de Mathématiques Pures et Appliquées, 2013, 100 (2), pp.241-274. ⟨hal-00675594⟩
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