KINETICS OF HETEROGENEOUS SINGLE-SPECIES ANNIHILATION

We investigate the kinetics of diffusion-controlled heterogeneous sing le-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusi on coefficient has the same time dependence as in homogeneous single-s pecies annihilation A + A --> 0. However, the concentrations of more m obile species decay as power laws in time, but with nonuniversal expon ents that depend on the ratios of the corresponding diffusivities to t hat of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimensio n d > 2, and in a phenomenological Smoluchowski theory, which is appli cable in d < 2. Our theoretical predictions compare well with both Mon te Carlo simulations and time series expansions.