Universal behavior for single-file diffusion on a disordered fractal

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 a 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.