Deconstructing symmetry breaking dynamics

TL;DR

This paper analyzes the dynamics of symmetry breaking during phase transitions, providing analytical insights into the Kibble-Zurek mechanism and proposing new observable tests to better understand defect formation.

Contribution

It offers an analytical solution to the Landau-Ginzburg model explaining the role of order parameter evolution in symmetry breaking, and suggests new experimental observables.

Findings

Analytical solutions elucidate the role of order parameter dynamics.

Proposes novel observables to test symmetry breaking theories.

Enhances understanding of defect formation during phase transitions.

Abstract

The Kibble-Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant $\hat t$ when the order parameter catches up with the post-transition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well we analyze Landau-Ginzburg model and show why temporal evolution of the order parameter plays such a key role. The analytical solutions we obtain suggest novel, hitherto unexplored, experimentally accessible observables that can shed light on symmetry breaking dynamics while testing the conjecture on which the KZM is based.