# Dynamics of kinks: nucleation, diffusion and annihilation

Physical Review Letters 84 1070 (2000)

#### Salman Habib

T8
Los Alamos National Laboratory
NM87545, USA.

#### G.D. Lythe

Centre for Nonlinear Studies
Los Alamos National Laboratory
NM87545, USA.

## 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 {\em 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.