Acceleration from a clustering environment

TL;DR

This paper investigates how correlations in a random environment, modeled by the 1D Ising model, influence the asymptotic speed of a random walker, revealing a nonperturbative acceleration effect.

Contribution

It demonstrates that correlations in a slowly cooling environment can modify the walker's speed, providing exact results and insights into nonperturbative effects.

Findings

Correlations affect the walker's asymptotic speed.

Slow cooling environments lead to acceleration effects.

Exact results are obtained for the 1D Ising model environment.

Abstract

We study the effects of correlations in a random environment on a random walker. The dependence of its asymptotic speed on the correlations is a nonperturbative effect as it is not captured by a homogeneous version of the same environment. For a slowly cooling environment, the buildup of correlations modifies the walker's speed and, by so, realizes acceleration. We remark on the possible relevance in the discussion of cosmic acceleration as traditionally started from the Friedmann equations, which, from a statistical mechanical point of view, would amount to a mean-field approximation. Our environment is much simpler though, with transition rates sampled from the one-dimensional Ising model and allowing exact results and detailed velocity characteristics.