Smoothly-varying hopping rates in driven flow with exclusion

TL;DR

This paper analyzes a one-dimensional TASEP model with smoothly varying hopping rates, providing theoretical solutions and numerical validation for steady-state densities, currents, and phase boundaries under different boundary conditions.

Contribution

It introduces a mean field/adiabatic approximation for TASEP with position-dependent rates and confirms predictions through detailed numerical simulations.

Findings

Steady-state density profiles match theoretical predictions.

Currents are accurately predicted by the model.

Phase boundaries are confirmed with high numerical accuracy.

Abstract

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.