Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

TL;DR

This paper investigates a 1D Dirac operator with Bernoulli potentials, revealing conditions under which dynamical delocalization occurs despite the absence of continuous spectrum, contrasting with typical localization behavior.

Contribution

It introduces a 1D Bernoulli Dirac model and demonstrates the occurrence of dynamical delocalization at specific energies, expanding understanding of localization phenomena in relativistic quantum systems.

Findings

Zero mass case shows absence of dynamical localization at certain energies.

System is localized for most energies regardless of mass.

Dynamical delocalization occurs even without continuous spectrum.

Abstract

An 1D tight-binding version of the Dirac equation is considered; after checking that it recovers the usual discrete Schr?odinger equation in the nonrelativistic limit, it is found that for two-valued Bernoulli potentials the zero mass case presents absence of dynamical localization for 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.