Tracer diffusion on a crowded random Manhattan lattice

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 ∼ 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, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution 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.

Keywords

• random Manhattan lattice
• tracer diffusion
• hard-core lattice gas
• simple exclusion process
• quenched versus dynamical disorder