# Single-file transport in periodic potentials: The Brownian asymmetric exclusion process

## TL;DR

This paper investigates the collective dynamics of Brownian particles in periodic potentials, revealing how particle size and density influence steady-state currents and phase behavior, with implications for understanding single-file transport.

## Contribution

It introduces a comprehensive analysis of the Brownian asymmetric simple exclusion process, including general properties, phase predictions, and the impossibility of current reversals in certain driven systems.

## Key findings

- Average currents vary with particle size and density.
- Extremal current principles predict nonequilibrium phases.
- Current reversals are impossible in systems driven by constant drag or traveling waves.

## Abstract

Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models, where hard spheres are driven by a constant drag force through a periodic potential. Here, we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.