Inhomogeneous exclusion processes with extended objects: The effect of defect locations

TL;DR

This paper investigates how local inhomogeneities, such as slow sites, affect the steady state and current in a TASEP with particles of various sizes, revealing location-dependent effects and phenomena when multiple defects are present.

Contribution

It provides a comparative analysis of the impact of slow sites on TASEP with extended objects, highlighting the significance of defect location and interactions between multiple defects.

Findings

Current depends on slow site location for single defects.

Multiple slow sites can cause dramatic current drops when close.

Asymptotic behavior analyzed as defect rate approaches zero.

Abstract

We study the effects of local inhomogeneities, i.e., slow sites of hopping rate $q<1$, in a totally asymmetric simple exclusion process (TASEP) for particles of size $\ell \geq 1$ (in units of the lattice spacing). We compare the simulation results of $\ell =1$ and $\ell >1$ and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the \emph{location} of the slow site for both $\ell =1$ and $\ell >1$ cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, we study the asymptotic behavior when $q\to 0$. We also explore the associated density profiles and compare our findings to an earlier study using a simple mean-field theory. We then outline the biological significance of these effects.