Properties of periodic Hartree�Fock minimizers

Ghimenti, Marco; Lewin, Mathieu
May 2009
Calculus of Variations & Partial Differential Equations;May2009, Vol. 35 Issue 1, p39
Academic Journal
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 Poincar� Anal Non Lin�aire 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.


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