Persistence effects in deterministic diffusion

TL;DR

This paper investigates how persistence influences diffusion in deterministic systems, demonstrating how to incorporate memory effects into models of particle movement in billiard tables to improve diffusion coefficient estimates.

Contribution

It introduces a method to account for memory effects in diffusion models by including one- and two-step persistence, improving understanding of deterministic diffusion.

Findings

Persistence significantly affects diffusion coefficients.

Memory effects can be systematically included in models.

Enhanced models better match observed diffusion behavior.

Abstract

In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.