  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.
