Spectral and Localization Properties for the One-Dimensional Bernoulli Discrete Dirac Operator

Details Spectral and Localization Properties for the One-Dimensional Bernoulli Discrete Dirac Operator Spectral and Localization Properties for the One-Dimensional Bernoulli Discrete Dirac Operator

2005-05-18

arxiv.org/abs/math-ph/0505046v1

Physics

Mathematical Physics

no figure; 24 pages; to appear in Journal of Mathematical Physics

Scientific paper

10.1063/1.1948328

A 1D Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schr?odinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for all values of the mass, it is shown that its spectrum is pure point, whereas the zero mass case presents dynamical delocalization for specific values of the energy. The massive case presents dynamical localization (excluding some particular values of the energy). Finally, for general potentials the dynamical moments for distinct masses are compared, especially the massless and massive Bernoulli cases.

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