Properties of the periodic Hartree-Fock minimizer
Mathematical Physics
2008-12-18 v1 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0803.3269,
title = {Properties of the periodic Hartree-Fock minimizer},
author = {Marco Ghimenti and Mathieu Lewin},
journal= {arXiv preprint arXiv:0803.3269},
year = {2008}
}