Roberto Prado

Dynamical delocalization for the 1D Bernoulli discrete Dirac operator

A 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schrodinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero-mass case presents the absence of dynamical localization for some specific values of the energy, albeit it has no continuous spectrum. For the other energy values (again excluding some very specific ones) the Bernoulli–Dirac system is localized, independently of the mass.

Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator

An one-dimensional (1D) Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schrodinger 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.

Sparse one-dimensional discrete Dirac operators II: Spectral properties

We study spectral properties of some discrete Dirac operators with nonzero potential only at some sparse and suitably randomly distributed positions. As observed in the corresponding Schrodinger operators, we determine the Hausdorff dimension of its spectral measure and identify a sharp spectral transition from point to singular continuous.