Random walk approach to the d-dimensional disordered Lorentz gas

TL;DR

This paper develops an analytic expression for the diffusion constant in a disordered Lorentz gas using a correlated random walk approach, validated by numerical simulations across multiple dimensions.

Contribution

It introduces a novel analytic formula for the diffusion constant in disordered Lorentz gases applicable in any dimension, improving upon previous theoretical predictions.

Findings

The derived diffusion constant matches simulations in 2D and 3D.

The formula is exact in the dilute limit.

It provides better estimates than previous theories at higher densities.

Abstract

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.