Dynamical Localization for Discrete Anderson Dirac Operators

We 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 op...

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Detalles Bibliográficos
Autores: Prado, Roberto A. [UNESP], de Oliveira, César R., Carvalho, Silas L.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/169502
Acceso en línea:http://dx.doi.org/10.1007/s10955-017-1746-6
http://hdl.handle.net/11449/169502
Access Level:acceso abierto
Palabra clave:Anderson Dirac operators
Dynamical localization
Fractional moments method
Descripción
Sumario:We 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.