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hal.structure.identifierLaboratoire Ondes et Matière d'Aquitaine [LOMA]
dc.contributor.authorDEAN, David S.
hal.structure.identifierLaboratoire de Physique Théorique de l'ENS [École Normale Supérieure] [LPTENS]
dc.contributor.authorLE DOUSSAL, Pierre
hal.structure.identifierLaboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
dc.contributor.authorMAJUMDAR, Satya. N.
hal.structure.identifierLaboratoire de Physique Théorique et Modèles Statistiques [LPTMS]
dc.contributor.authorSCHEHR, Gregory
dc.date.created2016-12-12
dc.date.issued2017-06-07
dc.identifier.issn1742-5468
dc.description.abstractEnWe consider N non-interacting fermions in an isotropic d-dimensional harmonic trap. We compute analytically the cumulative distribution of the maximal radial distance of the fermions from the trap center at zero temperature. While in d = 1 the limiting distribution (in the large N limit), properly centered and scaled, converges to the squared Tracy–Widom distribution of the Gaussian unitary ensemble in random matrix theory, we show that for all d > 1, the limiting distribution converges to the Gumbel law.These limiting forms turn out to be universal, i.e. independent of the details of the trapping potential for a large class of isotropic trapping potentials. We also study the position of the right-most fermion in a given direction in d dimensions and, in the case of a harmonic trap, the maximum momentum, and show that they obey similar Gumbel statistics. Finally, we generalize these results to low but finite temperature.
dc.language.isoen
dc.publisherIOP Publishing
dc.rights.urihttp://creativecommons.org/licenses/by-sa/
dc.subject.enExtreme value statistics
dc.subject.enQuantum gases
dc.subject.enRandom matrix theory and extensions
dc.title.enStatistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
dc.typeArticle de revue
dc.identifier.doi10.1088/1742-5468/aa6dda
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
dc.subject.halPhysique [physics]/Matière Condensée [cond-mat]/Gaz Quantiques [cond-mat.quant-gas]
dc.subject.halPhysique [physics]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv1612.03954
bordeaux.journalJournal of Statistical Mechanics: Theory and Experiment
bordeaux.page063301 (1-39)
bordeaux.volume2017
bordeaux.issue6
bordeaux.peerReviewedoui
hal.identifierhal-01558139
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01558139v1
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