Dynamical localization of Dirac particles in electromagnetic fields with dominating magnetic potentials

TL;DR

This paper investigates the conditions under which two-dimensional massless Dirac particles exhibit dynamical localization in electromagnetic fields, specifically when magnetic potentials dominate electric potentials at infinity, leading to dense point spectrum.

Contribution

It demonstrates dynamical localization for Dirac particles in radially symmetric electromagnetic fields with dominating magnetic potentials, expanding understanding of spectral properties in such systems.

Findings

Dynamical localization occurs when electric potential grows slower than magnetic potential at infinity.

Dense point spectrum is associated with the localization regime.

The results apply to radially symmetric electromagnetic fields with specific potential ratios.

Abstract

We consider two-dimensional massless Dirac operators in a radially symmetric electromagnetic field. In this case the fields may be described by one-dimensional electric and magnetic potentials $V$ and $A$. We show dynamical localization in the regime when $\displaystyle\lim_{r\to\infty}|V|/|A |<1$, where dense point spectrum occurs.