Tracer Diffusion on a Crowded Random Manhattan Lattice

TL;DR

This study uses extensive simulations to analyze the super-diffusive behavior and displacement distribution of a tracer particle in a crowded, disordered environment with random flows, revealing persistent Gaussian and non-Gaussian features.

Contribution

It provides novel insights into tracer diffusion dynamics on a crowded random Manhattan lattice, highlighting super-diffusive behavior and distribution characteristics under different disorder conditions.

Findings

Tracer exhibits super-diffusive mean-squared displacement ~ t^{4/3}.

Displacement distribution has a Gaussian core with non-Gaussian tails.

Crowded environment preserves distribution features despite disorder.

Abstract

We study by extensive numerical simulations the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder - frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour $\sim t^{4/3}$, $t$ being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position $X$ along the $x$-axis. Our analysis evidences that in absence of the lattice gas particles the latter has a Gaussian central part $\sim \exp(- u^2)$, where $u = X/t^{2/3}$, and exhibits slower-than-Gaussian tails $\sim \exp(-|u|^{4/3})$ for sufficiently large $t$ and $u$. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.