Droplet nucleation and domain wall motion in a bounded interval

We study a spatially extended model of noise-induced magnetization reversal: a classical Ginzburg-Landau model, restricted to a bounded interval and perturbed by weak spatiotemporal noise. By adapting the Coleman-Langer approach to false vacuum decay, we determine the dependence of the activation barrier and Kramers rate prefactor on the interval length. As it increases, a transition between activation regimes occurs, at which the prefactor diverges. Similar transitions between activation regimes should occur in many other bistable, spatially extended classical models.