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

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.