Dynamics of kinks: nucleation, diffusion and annihilation

Physical Review Letters 84 1070 (2000)

Salman Habib

Los Alamos National Laboratory
NM87545, USA.

G.D. Lythe

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


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.

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