Brownian asymmetric simple exclusion process

TL;DR

This paper investigates the steady-state behavior of driven Brownian particles with hard-core interactions in a periodic potential, revealing complex current-density relations and phase transitions influenced by particle size.

Contribution

It introduces a detailed analysis of how particle size affects current and phase behavior in driven Brownian systems within a cosine potential, highlighting novel phenomena and phase transitions.

Findings

Current-density relation varies with particle size, showing maxima and minima.

Five distinct non-equilibrium phases identified in open systems.

Particle size critically influences phase transitions and steady states.

Abstract

We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking and exchange symmetry effect. The latter leads to a current equal to that of non-interacting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of non-equilibrium steady states to occur. Our results show that the particle size can be of crucial importance for non-equilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.