Jamming of multiple persistent random walkers in arbitrary spatial dimension

TL;DR

This paper studies how persistent random walkers interact and jam in arbitrary dimensions, revealing that clustering can occur at very low densities in the ballistic regime, contrasting with diffusive behavior.

Contribution

It introduces an approximation for the mean first-passage time to jamming in a persistent exclusion process and generalizes findings to many-particle systems in arbitrary dimensions.

Findings

Mean first-passage time to jammed state calculated for two particles.

Approximation validated by numerical simulations even for small lattices.

Clusters can form at arbitrarily low densities in the ballistic regime.

Abstract

We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in the same direction over many lattice sites before reorienting. In the case of two particles, we find the mean first-passage time to a jammed state where the particles occupy adjacent sites and face each other. This is achieved within an approximation that amounts to embedding the one-dimensional system in a higher-dimensional reservoir. Numerical results demonstrate the validity of this approximation, even for small lattices. The results admit a straightforward generalisation to dilute systems comprising more than two particles. A self-consistency condition on the validity of these results suggest that clusters may form at arbitrarily low densities in the ballistic regime, in contrast to what has been found in the diffusive limit.