Properties of periodic Hartree–Fock minimizers

  • Marco Ghimenti
  • Mathieu Lewin


We study the periodic Hartree–Fock model used for the description of electrons in a crystal. The existence of a minimizer was previously shown by Catto et al. (Ann Inst H Poincaré Anal Non Linéaire 18(6):687–760, 2001). We prove in this paper that any minimizer is necessarily a projector and that it solves a certain nonlinear equation, similarly to the atomic case. In particular we show that the Fermi level is either empty or totally filled.

Mathematics Subject Classification (2000)

49S05 36P30 81Q10 81V55 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica Applicata “Ulisse Dini”Università di PisaPisaItaly
  2. 2.CNRS and Department of Mathematics UMR8088University of Cergy PontoiseCergy Pontoise CedexFrance

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