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

TL;DR

This study numerically investigates how the density of topological defects scales with quench rate in driven disordered systems, demonstrating the applicability of the Kibble-Zurek mechanism to nonequilibrium phase transitions.

Contribution

It shows that defect density scales as a power law with quench time and connects the scaling exponent to the directed percolation universality class, extending Kibble-Zurek theory.

Findings

Defect density scales as 1/t_q^β with β consistent across disorder strengths.

Scaling exponent linked to directed percolation universality class.

Kibble-Zurek mechanism applies to nonequilibrium phase transitions in disordered systems.

Abstract

We numerically study the density of topological defects for a two-dimensional assembly of particles driven over quenched disorder as a function of quench rate through the nonequilibrium phase transition from a plastic disordered flowing state to a moving anisotropic crystal. A dynamical ordering transition of this type occurs for vortices in type-II superconductors, colloids, and other particle-like systems in the presence of random disorder. We find that on the ordered side of the transition, the density of topological defects $\rho_d$ scales as a power law, $\rho_d \propto 1/t_{q}^\beta$, 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 show that scaling with the same exponent holds for varied strengths of quenched disorder. The value of the exponent can be connected to the directed percolation universality class. Our results suggest that the Kibble-Zurek mechanism can be applied to general nonequilibrium phase transitions.