Full Counting Statistics of Topological Defects After Crossing a Phase Transition

TL;DR

This paper analyzes the full counting statistics of topological defects formed during a continuous phase transition, revealing universal scaling laws and distribution properties beyond the mean defect number.

Contribution

It introduces a binomial distribution model for defect statistics and predicts universal power-law scaling of all cumulants with quench time.

Findings

Defect distribution follows a binomial model.

All cumulants exhibit universal power-law scaling.

Distribution analysis informs about adiabaticity and rare events.

Abstract

We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism. Statistics of defects follows a binomial distribution with $\mathcal{N}$ Bernouilli trials associated with the probability of forming a topological defect at the locations where multiple domains merge. All cumulants of the distribution are predicted to exhibit a common universal power-law scaling with the quench time in which the transition is crossed. Knowledge of the distribution is used to discuss the onset of adiabatic dynamics and bound rare events associated with large deviations.