Diffusive propagation of wave packets in a fluctuating periodic potential
Eman Hamza, Yang Kang, Jeffrey Schenker
TL;DR
This paper studies how wave packets evolve in a fluctuating periodic potential, demonstrating that their squared amplitude converges to a heat equation solution under certain conditions, indicating diffusive behavior.
Contribution
It establishes a rigorous connection between wave packet evolution in a stochastic potential and diffusive heat equation limits, under Markovian fluctuations.
Findings
Wave packet squared amplitude converges to a heat equation solution
Diffusive behavior emerges in the presence of Markovian potential fluctuations
Provides a mathematical framework for wave propagation in random media
Abstract
We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.
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