Nucleation rate of kink-antikink pairs in a driven and overdamped deformable chain

Abstract

The equilibrium nucleation rate of thermally activated kink-antikink pairs, in nonlinear deformable substrate potential systems coupled to an external applied field, is determined analytically at low temperature, and in the limit of strong damping. We focus our attention on a class of parametrized one-site potential ${V}_{\mathrm{RP}}(u,r)$ whose shape can be varied as a function of parameter $r$ and which has the sine-Gordon shape as the particular case. We derive the driven kink velocity as well as the average velocity of the displacement of a particle as a function of an applied field. We show that for a given temperature this average velocity not only depends on the external field, but also on the shape parameter $r.$ The model is used to describe the diffusion of atoms on metallic surfaces. Numerical values are estimated for the diffusion of hydrogen in tungsten (W) and ruthenium (Ru) substrates.