Diffusion and subdiffusion of interacting particles on comb-like structures

TL;DR

This paper investigates the complex dynamics of a tracer particle on comb-like structures with interacting particles, revealing multiple subdiffusive regimes, a transition to normal diffusion, and the surprising effect of interactions speeding up particle motion.

Contribution

It provides exact analytical results for tracer particle behavior on comb lattices and introduces a mean-field approach to describe multiple subdiffusive regimes influenced by geometry and interactions.

Findings

Subdiffusive behavior with exponent 3/4 on the backbone at high density

Transition to normal diffusion with a non-analytical density dependence

Interactions accelerate tracer particle motion across regimes

Abstract

We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only, and, in the limit of high density of particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior $\sim t^{3/4}$. At longer times, a second regime is observed, where standard diffusion is recovered, with a surprising non analytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like Continuous Time Random Walk description, we unveil a rich and complex scenario, with several successive subdiffusive regimes, resulting from the coupling between the inhomogeneous comb geometry and particle interactions. Remarkably, the presence of hard-core interactions speeds up the TP motion along the backbone of the structure in all regimes.