Structure and diffusion time scales of disordered clusters

TL;DR

This paper investigates how random walks on critically disordered clusters exhibit a transition from disordered to Euclidean-like behavior over different time scales, revealing insights into the structure and diffusion processes in such systems.

Contribution

It introduces an analysis of eigenvalue spectra of transition matrices to understand the evolving geometry and diffusion time scales in disordered clusters.

Findings

Eigenvalue spectra indicate a developing Euclidean signature at short time scales.

Disordered clusters show a transition in diffusion behavior as local constraints are applied.

The study compares three types of percolation problems to generalize the findings.

Abstract

The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for short time scales as the local, full-coordination constraint is iteratively applied.