Exploring the Kibble-Zurek mechanism in a secondary bifurcation

TL;DR

This study investigates the dynamics of a thermo-convective system undergoing a secondary bifurcation, revealing how different quenching rates influence defect formation and correlation lengths, akin to the Kibble-Zurek mechanism.

Contribution

It provides experimental evidence of the Kibble-Zurek mechanism in a complex, extended system during a secondary bifurcation, highlighting the role of quench rate in defect dynamics.

Findings

Fast quenches produce defect trapping at the front.

Correlation length scales follow a power-law dependence on quench rate.

Different relaxation mechanisms are observed depending on the crossing rate.

Abstract

We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a dynamical phase transition through the nature of the domain walls (1D-fronts) that connect the basic multicellular pattern with the new oscillating one. Two different mechanisms of the relaxing dynamics at the threshold are characterized depending on the crossing rate $\mu=\frac{d\epsilon}{dt}|_{\epsilon=0}$ (where $\epsilon$ is the control parameter) of the quenched transition. From the analysis of fronts, we show that these mechanisms follow different correlation length scales $\xi \sim \mu^{-\sigma}$. Below a critical value $\mu_c$ a slow response dynamics yields a spatiotemporal coherent front with weak coupling between oscillators. Above $\mu_c$, for rapid quenches, defects are trapped at the front with a strong coupling between oscillators, similarly to the Kibble-Zurek mechanism in quenched phase transitions. These defects, which are pinned to the fronts, yield a strong decay of the correlation length.