Unifying Kibble-Zurek Mechanism in Weakly Driven Processes

TL;DR

This paper introduces a new framework for the Kibble-Zurek mechanism that eliminates ad hoc hypotheses, providing a more unified understanding of the scaling behavior in driven systems near critical points.

Contribution

The work develops a novel theoretical framework for the Kibble-Zurek mechanism that removes the need for previous ad hoc assumptions, applicable to various system types.

Findings

Kibble-Zurek scaling for excess work is approximately 2/5.

Framework applies to open and thermally isolated systems.

Validated with four different scaling functions.

Abstract

A description of the Kibble-Zurek mechanism with linear response theory has been done previously, but ad hoc hypotheses were used, like the use of the rate-dependent impulse window via the Zurek equation in the context of no driving in the relaxation time. In this work, I present a new framework where such hypotheses are unnecessary, preserving all the characteristics of the phenomenon. The Kibble-Zurek scaling obtained for the excess work is close to 2/5, a result that holds for open and thermally isolated systems whose relaxation time diverges at the critical point and the first zero of the relaxation function is finite. I exemplify the results using four different but significant types of scaling functions.