  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.

Statistical Mechanics;Superconductivity;High Energy Physics - Theory