Kibble Zurek mechanism in rapidly quenched phase transition dynamics

TL;DR

This paper develops a theory explaining deviations from the Kibble-Zurek mechanism in rapid quenches, identifying a critical quench rate and deriving scaling laws verified through AdS/CFT in superconducting rings.

Contribution

It introduces a new theoretical framework for understanding KZM deviations in rapid quenches, including a critical quench rate and specific scaling laws.

Findings

Defect density becomes temperature-dependent below a critical quench rate.

Scaling laws for freeze-out time are confirmed in superconducting rings.

Critical quench rate depends on final temperature and critical exponents.

Abstract

We propose a theory to explain the experimental observed deviation from the Kibble-Zurek mechanism (KZM) scaling in rapidly quenched critical phase transition dynamics. There is a critical quench rate $\tau_{Q}^{c1}$ above it the KZM scaling begins to appear. Smaller than $\tau_Q^{c1}$, the defect density $n$ is a constant independent of the quench rate but depends on the final temperature $T_f$ as $n \propto L^d \epsilon_{T_f} ^{d \nu}$, the freeze out time $\hat{t}$ admits the scaling law $\hat{t} \propto \epsilon_{T_f}^{-\nu z}$ where $d$ is the spatial dimension, $\epsilon_{T_f}= (1-T_f/T_c)$ is the dimensionless reduced temperature, $L$ is the sample size, $\nu$ and $z$ are spatial and dynamical critical exponents. Quench from $T_c$, the critical rate is determined by the final temperature $T_f$ as $\tau_Q^{c1} \propto \epsilon_{T_f}^{-(1+z \nu)} $. All the scaling laws are verified in a rapidly quenched superconducting ring via the AdS/CFT correspondence.