Dynamical Localization for Discrete Anderson Dirac Operators

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dc.contributor.authorPrado, Roberto A. [UNESP]
dc.contributor.authorde Oliveira, César R.
dc.contributor.authorCarvalho, Silas L.
dc.contributor.institutionUniversidade Federal de Santa Catarina (UFSC)
dc.contributor.institutionUniversidade Federal de São Carlos (UFSCar)
dc.contributor.institutionUniversidade Federal de Minas Gerais (UFMG)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2018-12-11T16:46:11Z
dc.date.available2018-12-11T16:46:11Z
dc.date.issued2017-04-01
dc.description.abstractWe establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d∈ {1 , 2 , 3 } , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the continuous Dirac operators and consist in the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by different scalar potentials, which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support. We prove the exponential decay of fractional moments of the Green function for such models in each of the above regimes, i.e., (j) throughout the spectrum at larger disorder, (jj) for energies near the band edges at arbitrary disorder and (jjj) in dimension one, for all energies in the spectrum and arbitrary disorder. Dynamical localization in theses regimes follows from the fractional moments method. The result in the one-dimensional regime contrast with one that was previously obtained for 1D Dirac model with Bernoulli potential.en
dc.description.affiliationDepartamento de Matemática UFSC
dc.description.affiliationDepartamento de Matemática UFSCar
dc.description.affiliationDepartamento de Matemática UFMG
dc.description.affiliationUNESP
dc.description.affiliationUnespUNESP
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipIdCNPq: 157873/2015-3
dc.description.sponsorshipIdCNPq: 441004/2014-8
dc.format.extent260-296
dc.identifierhttp://dx.doi.org/10.1007/s10955-017-1746-6
dc.identifier.citationJournal of Statistical Physics, v. 167, n. 2, p. 260-296, 2017.
dc.identifier.doi10.1007/s10955-017-1746-6
dc.identifier.file2-s2.0-85014091476´.pdf
dc.identifier.issn0022-4715
dc.identifier.scopus2-s2.0-85014091476
dc.identifier.urihttp://hdl.handle.net/11449/169502
dc.language.isoeng
dc.relation.ispartofJournal of Statistical Physics
dc.relation.ispartofsjr0,930
dc.rights.accessRightsAcesso aberto
dc.sourceScopus
dc.subjectAnderson Dirac operators
dc.subjectDynamical localization
dc.subjectFractional moments method
dc.titleDynamical Localization for Discrete Anderson Dirac Operatorsen
dc.typeArtigo

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