An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

TL;DR

This paper develops an analytical approximation for the diffusion coefficient in the periodic Lorentz gas, improving upon previous models and aligning well with numerical data.

Contribution

It introduces a new stochastic model and an extremum principle to derive a closed-form approximation for the diffusion coefficient.

Findings

The approximation outperforms the Machta and Zwanzig result.

The model agrees well with numerical estimates.

Provides a practical analytical tool for studying diffusion in Lorentz gases.

Abstract

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.