Kibble-Zurek Mechanism for Nonequilibrium Phase Transitions in Driven Systems with Quenched Disorder

We examine the density of topological defects for a two-dimensional particle assembly driven over quenched disorder for varied quench rates across a nonequilibrium phase transition from a plastic disordered flowing state to a moving anisotropic crystal. This type of dynamical ordering transition occurs for vortices in type-II superconductors, colloidal particles, and other particle-like systems in the presence of random disorder. We find that the density of topological defects on the ordered side of the transition scales as a power law with the form 1/t_q^β, where t_q is the time duration of the quench across the transition. This type of scaling is predicted in the Kibble-Zurek mechanism for varied quench rates across a continuous phase transition. We find that the scaling behavior holds for varied strengths of quenched disorder with the same exponent in different systems. The value of the exponent can be connected to the directed percolation universality class. Our results also suggest that the Kibble-Zurek mechanism can be applied in general to nonequilibrium phase transitions.