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dc.contributor.authorRicaud, Julien
dc.date.accessioned2018-03-19T14:45:22Z
dc.date.available2018-03-19T14:45:22Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17575
dc.language.isoenen
dc.subjectThomas–Fermi–Dirac–von Weizsäcker modelen
dc.subjectSchrödinger equationen
dc.subject.ddc520en
dc.titleSymmetry breaking in the periodic Thomas–Fermi–Dirac–von Weizsäcker modelen
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider the Thomas--Fermi--Dirac--von~Weizsäcker model for a system composed of infinitely many nuclei placed on a periodic lattice and electrons with a periodic density. We prove that if the Dirac constant is small enough, the electrons have the same periodicity as the nuclei. On the other hand if the Dirac constant is large enough, the 2-periodic electronic minimizer is not 1-periodic, hence symmetry breaking occurs. We analyze in detail the behavior of the electrons when the Dirac constant tends to infinity and show that the electrons all concentrate around exactly one of the 8 nuclei of the unit cell of size 2, which is the explanation of the breaking of symmetry. Zooming at this point, the electronic density solves an effective nonlinear Schrödinger equation in the whole space with nonlinearity $u^{7/3}-u^{4/3}$. Our results rely on the analysis of this nonlinear equation, in particular on the uniqueness and non-degeneracy of positive solutions.en
dc.identifier.citationpages41en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01487352en
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-03-19T14:43:32Z
hal.person.labIds60


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