Stochastic models of classical particle pumps : Density dependence of directed current

TL;DR

This paper investigates particle pump models with repulsive interactions, analyzing how directed current depends on density, potential, and frequency, revealing maximum currents at intermediate densities and current reversal phenomena.

Contribution

It introduces and compares different particle pump models with microscopic reversibility, providing perturbative expressions for current and exploring density-dependent behaviors.

Findings

Directed current vanishes at zero and close packing densities.

Maximum current occurs at intermediate densities for two hopping rate choices.

Current reversal observed with increasing density for a specific hopping rate choice.

Abstract

We present and compare different versions of a simple particle pump-model that describes average directed current of repulsively interacting particles in a narrow channel, due to time-varying local potentials. We analyze the model on discrete lattice with particle exclusion, using three choices of potential-dependent hopping rates that obey microscopic reversibility. Treating the strength of the external potential as a small parameter with respect to thermal energy, we present a perturbative calculation to obtain the expression for average directed current. This depends on driving frequency, phase, and particle density. The directed current vanishes as density goes to zero or close packing. For two choices of hopping rates, it reaches maximum at intermediate densities, while for a third choice, it shows a curious current reversal with increasing density. This can be interpreted in terms of a particle-hole symmetry. Stochastic simulations of the model show good agreement with our analytic predictions.