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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorGontier, David
HAL ID: 11393
ORCID: 0000-0001-8648-7910
hal.structure.identifierEcole Nationale Supérieure d'Electricité et de Mécanique [Casablanca] [ENSEM]
dc.contributor.authorLahbabi, Salma
dc.date.accessioned2019-09-02T11:05:35Z
dc.date.available2019-09-02T11:05:35Z
dc.date.issued2019
dc.identifier.issn0022-2488
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19622
dc.language.isoenen
dc.subjectDensity-matrixen
dc.subjectOperator theoryen
dc.subjectMagnetic energyen
dc.subjectPartial differential equationsen
dc.subjectProbability theoryen
dc.subjectMagnetic fieldsen
dc.subjectSelf consistent field methodsen
dc.subject.ddc520en
dc.titleThe reduced Hartree-Fock model with self-generated magnetic fieldsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the well-posedness of the reduced Hartree-Fock model for molecules and perfect crystals when taking into account a self-generated magnetic field. We exhibit a critical value αc > 0 such that if the fine structure constant α is smaller than αc, then the corresponding system is stable, whereas if α is greater than αc, it is unstable. We give an explicit characterization of αc as a minimization problem over the set of zero-modes, and we prove that the critical values for the molecular case and the periodic case coincide. Finally, we prove the existence of minimizers when the system is neutral or positively charged.en
dc.relation.isversionofjnlnameJournal of Mathematical Physics
dc.relation.isversionofjnlvol60en
dc.relation.isversionofjnlissue8en
dc.relation.isversionofjnldate2019-08
dc.relation.isversionofdoi10.1063/1.5100919en
dc.relation.isversionofjnlpublisherAmerican Institute of Physicsen
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-09-02T09:51:33Z
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