Nucleation theory of overdamped soliton motion

We consider a ring of tightly torsion-coupled, overdamped pendulums subject to an external torque and coupled to a thermal reservoir. At low temperatures the dynamics of this system, over a wide range of forces, is governed by thermally activated kink-antikink pairs, their subsequent separation through the external force, and eventual recombination by collision with other kinks. We calculate the thermal activation rate of kink-antikink pairs using an approach first developed by Brinkman. This theory requires a detailed investigation of the multidimensional saddle, which has to be crossed, if the system is to make a thermally activated transition. The propagation velocity of the driven kinks is calculated. We use these results to derive the mean angular pendulum velocity as a function of the applied torque. Comparison is made with earlier work.