Properties of the periodic Hartree-Fock minimizer

Ghimenti, Marco; Lewin, Mathieu

Ghimenti, Marco; Lewin, Mathieu (2009), Properties of the periodic Hartree-Fock minimizer, Calculus of Variations and Partial Differential Equations, 35, 1, p. 39-56. http://dx.doi.org/10.1007/s00526-008-0196-z

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00266413/en/

Date

2009

Journal name

Calculus of Variations and Partial Differential Equations

Volume

Number

Publisher

Springer

Pages

39-56

Abstract (EN)

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.

Subjects / Keywords

Quantum Algebra; Mathematics