Particle current in symmetric exclusion process with time-dependent hopping rates

TL;DR

This paper investigates how periodic time-dependent hopping rates in a symmetric exclusion process can generate a significant net DC current, extending previous models and providing analytical insights through perturbation and sudden approximation methods.

Contribution

It generalizes earlier work by analyzing a model with all sites' hopping rates varying periodically, showing conditions for a substantial DC current using perturbation theory.

Findings

DC current of order unity for certain phase differences

Current decreases inversely with system size in previous models

Perturbation theory and sudden approximation methods validate results

Abstract

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.