Persistent random walk on a one-dimensional lattice with random asymmetric transmittances

TL;DR

This paper investigates how photons diffuse on a one-dimensional lattice with random asymmetric transmittances, using theoretical and simulation methods to identify conditions for normal diffusion.

Contribution

It introduces an effective medium approximation approach to analyze photon diffusion on a lattice with asymmetric transmittances and classifies distributions leading to normal diffusion.

Findings

Effective medium approximation predicts normal diffusion under certain transmittance distributions.

Monte Carlo simulations confirm the theoretical predictions.

Two classes of transmittance distributions are identified as leading to normal diffusion.

Abstract

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t') for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density Distribution. We use the effective medium approximation and identify two classes of probability density distribution of transmittances which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions.