  We use large scale simulations to study interacting particles in two
dimensions in the presence of both an ac drive and quenched disorder. As a
function of ac amplitude, there is a crossover from a low drive regime where
the colloid positions are highly disordered to a higher ac drive regime where
the system dynamically reorders. We examine the coarsening of topological
defects formed when the system is quenched from a disordered low ac amplitude
state to a high ac amplitude state. When the quench is performed close to the
disorder-order crossover, the defect density decays with time as a power law
with \alpha = 1/4 to 1/3. For deep quenches, in which the ac drive is increased
to high values such that the dynamical shaking temperature is strongly reduced,
we observe a logarithmic decay of the defect density into a grain boundary
dominated state. We find a similar logarithmic decay of defect density in
systems containing no pinning. We specifically demonstrate these effects for
vortices in thin film superconductors, and discuss implications for dynamical
reordering transition studies in these systems.
