  Driven diffusive systems constitute paradigmatic models of nonequilibrium
physics. Among them, a driven lattice gas known as the asymmetric simple
exclusion process (ASEP) is the most prominent example for which many
intriguing exact results have been obtained. After summarizing key findings,
including the mapping of the ASEP to quantum spin chains, we discuss the
recently introduced Brownian asymmetric simple exclusion process (BASEP) as a
related class of driven diffusive system with continuous space dynamics. In the
BASEP, driven Brownian motion of hardcore-interacting particles through
one-dimensional periodic potentials is considered. We study whether
current-density relations of the BASEP can be considered as generic for
arbitrary periodic potentials and whether repulsive particle interactions other
than hardcore lead to similar results. Our findings suggest that shapes of
current-density relations are generic for single-well periodic potentials and
can always be attributed to the interplay of a barrier reduction, blocking and
exchange symmetry effect. This implies that in general up to five different
phases of nonequilibrium steady states are possible for such potentials. The
phases can occur in systems coupled to particle reservoirs, where the bulk
density is the order parameter. For multiple-well periodic potentials, more
complex current-density relations are possible and more phases can appear.
Taking a repulsive Yukawa potential as an example, we show that the effects of
barrier reduction and blocking on the current are also present. The exchange
symmetry effect requires hardcore interactions and we demonstrate that it can
still be identified when hardcore interactions are combined with weak Yukawa
interactions.
