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

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 basic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. In this BASEP, hard rods are driven by a constant drag force through a periodic potential with an amplitude much larger than the thermal energy. Here we derive general properties of the collective dynamics in the BASEP, discuss its connection to single-file transport by traveling wave potentials, and give a complete description of currents in steady states for all particle densities and diameters. For the open BASEP coupled to particle reservoirs, the nonequilibrium phases predicted by extremal current principles are verified by Brownian dynamics simulations. * dlips@uos.de †

Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

“…II we present an analytical treatment of densities and currents for the overdamped one-dimensional Brownian motion of particles with arbitrary pair interactions. This section partly summarizes results presented earlier [55,56] and introduces the small-driving approximation used subsequently for our investigation of hardcore interacting particles. It also contains our proofs on the absence of current reversals for general pair interactions.…”

“…For hardcore interactions, the small-driving approximation (SDA) turned out to be particularly successful in capturing qualitative behaviors of j ss (ρ, σ) [56]. The approximation is carried out in two steps.…”

“…One is thus led to ask whether the driven diffusion of many hardcore interacting particles in a periodic energy landscape can reflect the driven lattice gas dynamics in the ASEP. To answer this question, we recently introduced a corresponding class of nonequilibrium processes termed Brownian ASEP (BASEP) [55,56], where hard spheres with diam-eter σ are driven through a periodic potential with wavelength λ by a constant drag force f . For a sinusoidal external potential, we found that the current-density relation of the ASEP is indeed recaptured in the BASEP, but only for a limited range of particle diameters σ.…”

“…Our investigation for the different external potentials are carried out based on the small-driving approximation introduced in Refs. [55] and [56]. With respect to short-range interactions other than hardcore exclusions, we focus on a Yukawa pair potential.…”

Hydrodynamic interactions can induce jamming in flow-driven systems

“…density. In addition, blocking effects can lead to a further slowing down with increasing ρ [28,29]. Indeed, we have seen indications of a hopping motion and jamming in the measured trajectories for large U 0 and high densities, see videos in the Supplemental Material [20].…”