Properties of the periodic Hartree-Fock minimizer

Details Properties of the periodic Hartree-Fock minimizer Properties of the periodic Hartree-Fock minimizer

2008-03-22

arxiv.org/abs/0803.3269v1

Physics

Mathematical Physics

Scientific paper

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, Le Bris and Lions (Ann. Inst. H. Poincare Anal. Non Lineaire} 18 (2001), no.6, 687--760). 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.

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