Density of kinks after a quench: When symmetry breaks, how big are the pieces?

TL;DR

This paper numerically investigates how the density of topological defects, specifically kinks, scales with quench rate during symmetry-breaking phase transitions, confirming a theoretical prediction about domain formation.

Contribution

It provides numerical evidence that the kink density scales as the fourth root of the quench rate, supporting a general theory of domain size evolution in symmetry breaking.

Findings

Kink density scales as the fourth root of the quench rate.

The results confirm the theoretical model of domain-size evolution.

The approach allows computation of defect density from quench timescale and critical scaling.

Abstract

Numerical study of order parameter dynamics in the course of second order (Landau-Ginzburg) symmetry breaking transitions shows that the density of topological defects, kinks, is proportional to the fourth root of the rate of the quench. This confirms the more general theory of domain-size evolution in the course of symmetry breaking transformations proposed by one of us \cite{Zurek85}. Using these ideas, it is possible to compute the density of topological defects from the quench timescale and from the equilibrium scaling of the correlation length and relaxation time near the critical point.