Dynamics of Kinks: Nucleation, Diffusion and Annihilation

TL;DR

This paper studies the behavior of kinks in a classical field theory at finite temperature, focusing on their nucleation, diffusion, and annihilation processes through simulations and analytical modeling.

Contribution

It introduces a mesoscopic model for diffusing kinks and provides analytical predictions that match simulation results, advancing understanding of kink dynamics.

Findings

Nucleation rate is proportional to the square of the equilibrium kink density.

Identifies two distinct annihilation time scales: recombination and non-recombinant annihilation.

Analytical predictions align well with large-scale Langevin simulation results.

Abstract

We investigate the nucleation, annihilation, and dynamics of kinks in a classical (1+1)-dimensional Phi^4 field theory at finite temperature. From large scale Langevin simulations, we establish that the nucleation rate is proportional to the square of the equilibrium density of kinks. We identify two annihilation time scales: one due to kink-antikink pair recombination after nucleation, the other from non-recombinant annihilation. We introduce a mesoscopic model of diffusing kinks based on ``paired'' and ``survivor'' kinks/antikinks. Analytical predictions for the dynamical time scales, as well as the corresponding length scales, are in good agreement with the simulations.