The Kibble-Zurek mechanism in a subcritical bifurcation

Abstract

We present the study of the freezing dynamics of topological defects in a subcritical system by testing the Kibble-Zurek (KZ) mechanism while crossing a tri-stable region in a one-dimensional quintic complex Ginzburg-Landau equation. The critical exponents of the KZ mechanism and the horizon (KZ-scaling regime) are predicted from the quasistatic study, and are in full accordance with the quenched study. The correlation length, in the KZ freezing regime, is corroborated from the number of topological defects and from the spatial correlation function of the order parameter. Furthermore, we characterize the dynamics to differentiate three out-of-equilibrium regimes: the adiabatic, the impulse and the free-relaxation. We show that the impulse regime shares a common temporal domain with a fast exponential increase of the order parameter.