Current-density relation in the exclusion process with dynamic obstacles

TL;DR

This paper studies a variant of the TASEP with dynamic obstacles, revealing a quasi-parabolic current-density relation similar to the standard TASEP, through simulations and exact calculations.

Contribution

It provides the first detailed analysis of the current-density relation in TASEP with dynamic obstacles, combining simulations and theoretical insights.

Findings

Current-density relation is quasi-parabolic, similar to standard TASEP.

Exact calculations explain the relation via cancellation of higher-order terms.

Simulation results support the theoretical findings.

Abstract

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasi-parabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasi-parabolic current-density relation arises through a non-trivial cancellation of higher-order terms, similarly as in the standard TASEP.