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

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