Density of Topological Defects After a Quench

TL;DR

This paper numerically investigates how the density of topological defects after a phase transition depends on the quench rate and relaxation dynamics, confirming a non-equilibrium domain formation mechanism.

Contribution

It demonstrates that defect density is determined by the interplay between quench rate and relaxation, extending the Kibble-Zurek mechanism to condensed matter analogues.

Findings

Defect density scales with quench rate and relaxation time.

Domain size is set by the correlation length at the freeze-out point.

The results support the non-equilibrium defect formation scenario.

Abstract

We present results of numerical studies of the Landau-Ginzburg dynamics of the order parameter in one-dimensional models inspired by the condensed matter analogues of cosmological phase transitions. The main goal of our work is to show that, as proposed by one of us \cite{Zurek85b}, the density of the frozen-out topological defects is set by the competition between the quench rate --- the rate at which the phase transition is taking place --- and the relaxation rate of the order parameter. In other words, the characteristic domain size, which determines the typical separation of topological defects in the new broken symmetry phase, is of the order of the correlation length at the instant at which the relaxation timescale of the order parameter equals the time remaining to the phase transition. In estimating the size of topological domains, this scenario shares with the original Kibble mechanism the idea that topological defects will form along the boundaries of independently selected regions of the new broken symmetry vacuum. However, it derives the size of such domains from non-equilibrium aspects of the transition (quench rate), as opposed to Kibble's original proposal in which their size was estimated from the Ginzburg temperature above which thermally activated symmetry restoration can occur.