Iterated Function System and Diffusion in the Presence of Disorder and Traps

TL;DR

This paper investigates how disorder and traps affect diffusion in a one-dimensional lattice, revealing that the invariant measure is multifractal but becomes uniform under weak disorder, with implications for understanding diffusion processes.

Contribution

It introduces a discrete dynamical framework for analyzing escape probabilities in disordered lattices with traps, highlighting the multifractal nature of the invariant measure and its transition to uniformity.

Findings

Invariant measure is multifractal in disordered systems.

Weak disorder leads to a uniform invariant measure.

Implications for diffusion behavior in disordered media.

Abstract

The escape probability $\xi_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump probabilities. The invariant measure of the dynamics is found to be a multifractal. However the measure becomes uniform over the support when the disorder becomes weak for any non-zero trapping probability. Implications of our findings in terms of diffusion are discussed.