KINETICS OF HETEROGENEOUS SINGLE-SPECIES ANNIHILATION

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