Dynamics of kinks: Nucleation, diffusion, and annihilation

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 pail recombination after nucleation, the other from nonrecombinant annihilation. We introduce a mesoscopic model of diffusing kinks based on "paired" and "survivor": kinks and antikinks. Analytical predictions for the dynamical time scales, as well as the corresponding length stales, are in good agreement with thr simulations.