Persistent exclusion process with time-periodic drive

Abstract

We study a persistent exclusion process with time-periodic external potential on a 1d periodic lattice through numerical simulations. A set of run-and-tumble particles move on a lattice of length $L$ and tumbling probability $\gamma \ll 1$ and interact among each other via hardcore exclusion. The effect of the external potential has been modeled as a special site where the tumbling probability is $1$. We call it a "defect" site and move its location along the ring lattice with speed $u$. In the case of $\gamma=0$ the system goes to a jammed state when there is no defect. But introduction of the moving defect creates a strongly phase-separated state where almost all active particles are present in a single large cluster, for small and moderate $u$. This striking effect is caused by the long-range velocity correlation of the active particles, induced by the moving defect. For large $u$, a single large cluster is no longer stable and breaks into multiple smaller clusters. For nonzero $\gamma$ a competition develops between the timescales associated with tumbling and defect motion. While the moving defect attempts to create long-range velocity order, bulk tumbling tends to randomize the velocity alignment. If $\gamma$ is comparable to $u/L$, then a relatively small number of tumbles take place during the time the moving defect travels through the entire system. In this case, the defect has enough time to restore the order in the system and our simulations show that the long-range order in velocity and density survive for $\gamma$ values in this range. As $\gamma$ increases further, long range order is destroyed and the system develops multiple regions of high and low density. We characterize the density inhomogeneity in this case by measuring subsystem density fluctuations and present a heatmap in the $\gamma$-$u$ plane showing the regions with most pronounced density inhomogeneities.