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Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHuveneers, François
hal.structure.identifier
dc.contributor.authorTheil, Elias
dc.date.accessioned2020-01-06T13:51:57Z
dc.date.available2020-01-06T13:51:57Z
dc.date.issued2019
dc.identifier.issn0022-4715
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20378
dc.language.isoenen
dc.subjectStatistical physicsen
dc.subjectStatistical ensembleen
dc.subjectCondensationen
dc.subjectGlassen
dc.subject.ddc520en
dc.titleEquivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonianen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study mathematically the equilibrium properties of the Bose–Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and the grand-canonical ensembles for all allowed values of the density of particles ρ and density of energy ε . Moreover, given ρ , we show that the system undergoes a transition as ε increases, from a usual positive temperature state to the infinite temperature state where a macroscopic excess of energy condensates on a single site. Analogous results have been obtained by Chatterjee [6] for a closely related model. We introduce here a different method to tackle this problem, hoping that it reflects more directly the basic understanding stemming from statistical mechanics. We discuss also how, and in which sense, the condensation of energy leads to a glassy dynamics.en
dc.relation.isversionofjnlnameJournal of Statistical Physics
dc.relation.isversionofjnlvol177en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2019-12
dc.relation.isversionofjnlpages917–935en
dc.relation.isversionofdoi10.1007/s10955-019-02396-zen
dc.relation.isversionofjnlpublisherSpringeren
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.updated2020-01-06T13:26:24Z
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hal.author.functionaut


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