Quantum diffusion of a relativistic particle in a time-dependent random potential

TL;DR

This paper rigorously analyzes how a relativistic particle's wave packet diffuses in a time-dependent random potential, revealing ballistic spreading in contrast to superballistic diffusion in nonrelativistic cases, due to relativistic conservation laws.

Contribution

It provides a rigorous theoretical study showing relativistic effects suppress superballistic diffusion, contrasting with nonrelativistic behavior in similar random potentials.

Findings

Relativistic particle wave packet spreads ballistically over time.

Nonrelativistic case exhibits superballistic diffusion under similar conditions.

Relativistic conservation laws influence the diffusion behavior.

Abstract

We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads ballistically in contrast with the nonrelativistic case, which in the same situation exhibits superballistic diffusion. The relativistic suppression of wave packet diffusion is discussed in connection with statistical conservation laws that follow from relativistic dynamics.