Universal behavior for single-file diffusion on a disordered fractal

TL;DR

This paper investigates single-file diffusion on a disordered fractal lattice, revealing universal behavior across different regimes and deriving analytic expressions for crossover times based on system parameters.

Contribution

It introduces a universal framework for understanding diffusion regimes on fractal disordered lattices, with explicit analytic formulas for crossover times.

Findings

Three distinct diffusion regimes identified

Universal form characterizes mean-square displacement behavior

Analytic expressions for crossover times depending on density and lattice size

Abstract

We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly interacting particles, and saturation. The mean-square displacement of a tagged particle as a function of time follows a power law in each regime. The first crossover time $t_s$, between the first and the second regime, depends on the particle density. The other crossover time $t_l$, between the second and the third regime, depends on the lattice length. We find analytic expressions for these dependencies and show how the general behavior can be characterized by an universal form. We also show that the mean-square displacement of the center of mass presents two regimes; anomalous diffusion for times shorter than $t_l$, and normal diffusion for times longer than $t_l$. We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly interacting particles, and saturation. The mean-square displacement of a tagged particle as a function of time follows a power law in each regime. The first crossover time $t_s$, between the first and the second regime, depends on the particle density. The other crossover time $t_l$, between the second and the third regime, depends on the lattice length. We find analytic expressions for these dependencies and show how the general behavior can be characterized by an universal form. We also show that the mean-square displacement of the center of mass presents two regimes; anomalous diffusion for times shorter than $t_l$, and normal diffusion for times longer than $t_l$.