The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation

TL;DR

This paper demonstrates that by choosing an appropriate probability distribution for particle collision distances, the nonclassical diffusion equation can be exactly represented by the nonclassical linear Boltzmann equation in an infinite medium, preserving the true mean-squared free path.

Contribution

It introduces a method to exactly represent the nonclassical diffusion equation using the nonclassical Boltzmann equation with a specific collision distance distribution.

Findings

Exact representation of nonclassical diffusion by Boltzmann equation

Preservation of true mean-squared free path

Insight into previous results

Abstract

We show that, by correctly selecting the probability distribution function $p(s)$ for a particle's distance-to-collision, the nonclassical diffusion equation can be represented exactly by the nonclassical linear Boltzmann equation for an infinite homogeneous medium. This choice of $p(s)$ preserves the $true$ mean-squared free path of the system, which sheds new light on the results obtained in previous work.