A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case

Simple item page
dc.creatorCancès, Eric
dc.creatorDeleurence, Amélie
dc.creatorLewin, Mathieu
dc.date2007-02-21
dc.date2008-04-17
dc.date.accessioned2026-07-07T12:38:21Z
dc.date.available2026-07-07T12:38:21Z
dc.descriptionThis article is concerned with the derivation and the mathematical study of a new mean-field model for the description of interacting electrons in crystals with local defects. We work with a reduced Hartree-Fock model, obtained from the usual Hartree-Fock model by neglecting the exchange term. First, we recall the definition of the self-consistent Fermi sea of the perfect crystal, which is obtained as a minimizer of some periodic problem, as was shown by Catto, Le Bris and Lions. We also prove some of its properties which were not mentioned before. Then, we define and study in details a nonlinear model for the electrons of the crystal in the presence of a defect. We use formal analogies between the Fermi sea of a perturbed crystal and the Dirac sea in Quantum Electrodynamics in the presence of an external electrostatic field. The latter was recently studied by Hainzl, Lewin, Séré and Solovej, based on ideas from Chaix and Iracane. This enables us to define the ground state of the self-consistent Fermi sea in the presence of a defect. We end the paper by proving that our model is in fact the thermodynamic limit of the so-called supercell model, widely used in numerical simulations.
dc.descriptionFinal version, to appear in Comm. Math. Phys
dc.identifierhttps://arxiv.org/abs/math-ph/0702071
dc.identifierhttp://arxiv.org/abs/math-ph/0702071
dc.identifierCommunications in Mathematical Physics 281, 1 (2008) 129-177
dc.identifierdoi:10.1007/s00220-008-0481-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218730
dc.subjectMathematical Physics
dc.titleA new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
dc.typetext

Files

Collections

arXiv