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Dynamical Localization for Discrete Anderson Dirac Operators

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Abstract

We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with \(d\in \left\{ 1, 2, 3\right\} \), 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.

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Acknowledgements

RAP was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (Brazilian agency, under contract 157873/2015-3). CRdO was partially supported by CNPq (Universal Project 441004/2014-8). SLC thanks the partial support by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (Universal Project CEX-APQ-00554-13).

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Authors and Affiliations

  1. Departamento de Matemática, UFSC, Florianópolis, SC, 88040-900, Brazil

    Roberto A. Prado

  2. Departamento de Matemática, UFSCar, São Carlos, SP, 13560-970, Brazil

    César R. de Oliveira

  3. Departamento de Matemática, UFMG, Belo Horizonte, MG, 31270-901, Brazil

    Silas L. Carvalho

  4. UNESP, Presidente Prudente, SP, 19060-900, Brazil

    Roberto A. Prado

Authors
  1. Roberto A. Prado
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  2. César R. de Oliveira
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  3. Silas L. Carvalho
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Correspondence to César R. de Oliveira.

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Roberto A. Prado: On leave of absence from UNESP.

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Prado, R.A., de Oliveira, C.R. & Carvalho, S.L. Dynamical Localization for Discrete Anderson Dirac Operators. J Stat Phys 167, 260–296 (2017). https://doi.org/10.1007/s10955-017-1746-6

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  • DOI: https://doi.org/10.1007/s10955-017-1746-6

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