  We show in simulations that overdamped interacting particles in two
dimensions with a randomly disordered substrate can exhibit novel
nonequilibrium transport phenomena including a transverse ratchet effect, where
a combined dc drive and circular ac drive produce a drift velocity in the
direction transverse to the applied dc drive. The random disorder does not
break any global symmetry; however, in two dimensions, symmetry breaking occurs
due to the chirality of the circular drive. In addition to inducing the
transverse ratchet effect, increasing the ac amplitude also strongly affects
the longitudinal velocity response and can produce what we term an overshoot
effect where the longitudinal dc velocity is higher in the presence of the ac
drive than it would be for a dc drive alone. We also find a dynamical
reordering transition upon increasing the ac amplitude. In the absence of a dc
drive, it is possible to obtain a ratchet effect when the combined ac drives
produce particle orbits that break a reflection symmetry. In this case, as the
ac amplitude increases, current reversals can occur. These effects may be
observable for vortices in type II superconductors as well as for colloids
interacting with random substrates.
