Spatial localization and diffusion of Dirac particles and waves induced by random temporal medium variations

TL;DR

This study explores how random temporal variations in media induce localization and diffusion of Dirac particles and waves, revealing universal insulating behavior and wave localization phenomena.

Contribution

It provides the first exact analytical expressions for temporal reflectance in Dirac systems with random mass variations and demonstrates universal localization effects.

Findings

Wave packets localize and spread indefinitely due to randomness.

Reflectance becomes uniformly distributed in long-time limit.

Wave velocities decay to zero, indicating localization.

Abstract

Wave propagation in time-varying media has attracted significant attention for its innovative potential to control wave-matter interactions and to develop versatile active materials. While most research has focused on electromagnetic waves, studies on Dirac-type waves remain limited. In this work, we investigate temporal scattering in pseudospin-1/2 Dirac systems with random temporal mass variations. Using the invariant imbedding method, we derive exact expressions for temporal reflectance in both short- and long-time regimes. In the long-time limit, reflectance probabilities become uniformly distributed, and wave group velocities decay to zero, indicating spatial localization. Numerical simulations reveal that narrow wave pulses evolve into Gaussian shapes, with their centers localizing and their widths growing indefinitely due to diffusive behavior. This universal phenomenon is independent of the initial pulse profile and the statistical properties of the random mass. Our findings demonstrate that random temporal variations can induce insulating behavior in Dirac materials, offering potential applications in solid-state physics and optics.