Density of kinks just after a quench in an underdamped system

TL;DR

This paper analytically investigates how the density of kinks in an underdamped one-dimensional $4$ model depends on the quench rate, revealing different scaling laws for slow and rapid quenches.

Contribution

It provides a theoretical analysis of kink density scaling laws immediately after a quench in an underdamped $4$ model, highlighting new scaling behaviors.

Findings

Kink density scales with the square root of the quench rate for slow quenches.

Kink density scales with the cube root of the quench rate when the quench is faster than the relaxation time.

Analytical methods elucidate the transition between different scaling regimes.

Abstract

A quench in an underdamped one dimensional $\phi^4$ model is studied by analytical methods. The density of kinks just after the transition is proportional to the square root of the rate of the quench for slow quenches. If the quench is shorter that the relaxation time, then the density scales like the third root of the rate.