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. © 2008 Springer-Verlag.
Ghimenti, M., Lewin, M. (2009). Properties of the periodic Hartree-Fock minimizer. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009(1), 39-56 [10.1007/s00526-008-0196-z].
Properties of the periodic Hartree-Fock minimizer
GHIMENTI, MARCO GIPO;
2009
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 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. © 2008 Springer-Verlag.
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