Density of kinks just after a quench in an overdamped system

TL;DR

This paper investigates how the density of kinks in an overdamped one-dimensional phi^4 model depends on the quench rate, revealing different scaling laws based on boundary conditions and challenging existing theoretical predictions.

Contribution

It provides analytical and numerical evidence that kink density scales differently with quench rate depending on boundary conditions, questioning the Zurek scenario's critical exponent.

Findings

Kink density scales as the eighth root of the quench rate for free boundary conditions.

Kink density scales as the fourth root of the quench rate for periodic boundary conditions.

The Zurek scenario's predicted critical exponent is challenged by these results.

Abstract

A quench in an overdamped one dimensional $\phi^4$ model is studied by analytical and numerical methods. For an infinite system or a finite system with free boundary conditions, the density of kinks after the transition is proportional to the eighth root of the rate of the quench. For a system with periodic boundary conditions, it is proportional to the fourth root of the rate. The critical exponent predicted in Zurek scenario is put in question.