Single-file diffusion on self-similar substrates

TL;DR

This paper investigates how particles diffuse on a one-dimensional lattice with a self-similar pattern of hopping rates, revealing anomalous diffusion behaviors with oscillations and deriving analytical expressions confirmed by simulations.

Contribution

It introduces a model of single-file diffusion on self-similar substrates and analytically characterizes the anomalous diffusion exponents and oscillations.

Findings

Mean-square displacement follows anomalous power laws.

Oscillations in diffusion are logarithmic periodic.

Analytical exponents match Monte Carlo simulations.

Abstract

We study the single file diffusion problem on a one-dimensional lattice with a self-similar distribution of hopping rates. We find that the time dependence of the mean-square displacement of both a tagged particle and the center of mass of the system present anomalous power laws modulated by logarithmic periodic oscillations. The anomalous exponent of a tagged particle is one half of the exponent of the center of mass, and always smaller than 1/4. Using heuristic arguments, the exponents and the periods of oscillation are analytically obtained and confirmed by Monte Carlo simulations.