Stochastic acceleration in a random time-dependent potential

TL;DR

This paper investigates how a particle's kinetic energy grows over time in a high-dimensional random, time-dependent environment, showing it increases as a power law under certain conditions.

Contribution

It provides a rigorous analysis of the asymptotic growth rate of particle energy in a stochastic, time-dependent potential, extending understanding of stochastic acceleration phenomena.

Findings

Kinetic energy grows as t^{2/5} for dimensions greater than 5.

High initial velocity ensures the growth behavior with high probability.

Results apply to particles undergoing Markovian scattering in random environments.

Abstract

We study the long time behaviour of the speed of a particle moving in $\mathbb{R}^d$ under the influence of a random time-dependent potential representing the particle's environment. The particle undergoes successive scattering events that we model with a Markov chain for which each step represents a collision. Assuming the initial velocity is large enough, we show that, with high probability, the particle's kinetic energy $E(t)$ grows as $t^{\frac25}$ when $d>5$.