Coarsening by diffusion-annihilation in a bistable system driven by noise

The stochastic Ginzburg-Landau equation in one dimension is the simplest continuum model describing the spatio-temporal evolution of a bistable system in the presence of thermal noise. Relaxation to equilibrium in this model proceeds by coarsening of the field during which regions in the two stables phases separated by localized kinks grow on the average. It is shown that coarsening in the presence of thermal noise effects, however small, is drastically different than in the deterministic situation. Coarsening by noise can be mapped onto the problem of diffusion-annihilation of independent particles on the line by identifying the particle locations with the kink positions. The diffusion-annihilation process displays universal self-similar features which are analyzed in detail.