Diffusion of wave packets in a Markov random potential

TL;DR

This paper demonstrates that a wave packet in a Markov random potential exhibits diffusive behavior, with its amplitude converging to a heat equation solution after rescaling, revealing insights into quantum dynamics in stochastic environments.

Contribution

It establishes a rigorous connection between quantum wave packet evolution in Markov potentials and classical diffusion described by the heat equation.

Findings

Wave packet amplitude converges to a heat equation solution

Diffusive rescaling reveals classical behavior in quantum systems

Markov process potential induces diffusive dynamics

Abstract

We consider the evolution of a tight binding wave packet propagating in a time dependent potential. If the potential evolves according to a stationary Markov process, we show that the square amplitude of the wave packet converges, after diffusive rescaling, to a solution of a heat equation.