Transition state and Brownian motion theories of solitons

Abstract

We investigate some aspects of the nonequilibrium statistical mechanics of the φ4 and sine-Gordon models. In particular we focus on the single site process of hopping between stable states. As a first approximation we calculate the rate constant for this process using a generalization of classical transition state theory, finding that the transition state is a soliton, and the hopping process results from the free streaming translational motion of these solitons. We then consider the possibility that the solitons can interact with their surroundings such that their translational motion becomes Brownian. With this model we calculate the hopping correlation function, finding that in the limit of no friction it decays exponentially with the time constant predicted by transition state theory, and in the high friction limit it is exp (−αt1/2) corresponding to soliton diffusion.