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.