Abstract
Under the influence of noise, metastable states in spatially one-dimensional systems decay via nucleation of kink-antikink pairs. In a realistic sample, translational invariance is destroyed by the finite size of the sample and by the presence of localized impurities. This leads to a competition between homogeneous and heterogeneous nucleation, i.e., the generation of free kink-antikink pairs in the bulk and kink-antikink pairs pinned at the sample surface or at impurities. For systems that can be modeled by a bistable reaction-diffusion equation, we derive the rates of homogeneous and heterogeneous nucleation in the framework of Kramers theory. In particular, the critical sample length and the critical density of impurities associated with the crossover between qualitatively different types of nucleation are derived. The results concerning the crossover density of impurities turn out to depend strongly on how the impurities couple to the order-parameter field.
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