Kink dynamics in the weakly stochastic Ø4 model

Abstract

We describe how kink dynamics in a weakly stochastic, nonlinear Ø4 model can be understood by means of different analytical approaches. We first show how usual decompositions of the ifJ4 chain excitations into translation, internal-oscillation, and phonon modes are valid up to a certain time that depends on the noise strength. By means of this decomposition we study the effects of dynamical disorder in the system on soliton propagation. The pinning of a kink on an unperturbed-perturbed boundary is considered in the adiabatic approximation. We then compute how the radiation generated by the kink absorbs energy in a resonant way from the noise at times later than the validity limit of our approximation. We conclude with a discussion of our findings and some comments on open questions and further extensions of this work.