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 theory, restricted to a bounded interval and perturbed by weak spatiotemporal noise. We compute the activation barrier and Kramers prefactor. As the interval length increases, a transition between activation regimes occurs, at which the prefactor diverges. We relate this to transitions that occur in low-temperature quantum field theory.