# Transport in exclusion processes with one-step memory: density dependence and optimal acceleration

## TL;DR

This paper investigates how the movement of particles with memory in a lattice gas depends on density and persistence, revealing novel non-monotonic behaviors and an optimal density for maximum displacement.

## Contribution

It introduces a mean-field theory to explain non-monotonic MSD behavior in exclusion processes with one-step memory, including the discovery of an optimal density for particle displacement.

## Key findings

- MSD increases with persistence and decreases with density for positive persistence.
- Strong anti-persistence leads to non-monotonic MSD dependence on density.
- An optimal density exists where MSD is maximized under strong anti-persistence.

## Abstract

We study a lattice gas of persistent walkers, in which each site is occupied by at most one particle and the direction each particle attempts to move to depends on its last step. We analyse the mean squared displacement (MSD) of the particles as a function of the particle density and their persistence (the tendency to continue moving in the same direction). For positive persistence the MSD behaves as expected: it increases with the persistence and decreases with the density. However, for strong anti-persistence we find two different regimes, in which the dependence of the MSD on the density is non-monotonic. For very strong anti-persistence there is an optimal density at which the MSD reaches a maximum. In an intermediate regime, the MSD as a function of the density exhibits both a minimum and a maximum, a phenomenon which has not been observed before. We derive a mean-field theory which qualitatively explains this behaviour.