Kibble-Zurek mechanism in driven underdamped Brownian motion

TL;DR

This paper demonstrates the occurrence of the Kibble-Zurek mechanism in driven underdamped Brownian motion, revealing divergence in relaxation time and new scaling behaviors under specific conditions.

Contribution

It extends the Kibble-Zurek mechanism to a simple classical system, showing its relevance beyond quantum phase transitions.

Findings

Divergence of relaxation time in the system.

Identification of high-temperature initial conditions for the effect.

Discovery of a new Kibble-Zurek scaling at sudden processes.

Abstract

Kibble-Zurek mechanism is widely known to appear in the transverse-field quantum Ising chain in the thermodynamic limit at zero temperature, having notorious characteristics, like the divergence of its relaxation time. In this work, I present the same effect in a simple system, the driven underdamped Brownian motion. Using linear response theory, I show the appropriate limits where the Kibble-Zurek mechanism happens. The divergence of the relaxation time, the high-temperature condition in the initial thermal equilibrium state, a new Kibble-Zurek scaling at sudden processes, and the pausing effect in the optimal protocol are presented as consequences.