Kinetics of heterogeneous single-species annihilation.

The kinetics of diffusion-controlled single-species annihilation, A + A → 0, when each particle has the same diffusion coefficient is now well understood [1]. For spatial dimension d > 2, the kinetics may be accounted for by the rate equation which predicts that the density decays as t−1 in the long-time limit. For d ≤ 2, various phenomenological approaches predict that the density decays as t−d/2, but with logarithmic corrections appearing in d = 2. Accompanying this relatively slow kinetics is a spatial organization in which the probability of finding particles at small separations is reduced compared to a random distribution. In one dimension, exact solutions, either based on an occupation number formalism [2], or by mapping the reaction onto the kinetic Ising-Glauber model [3], provide definitive results about this spatial organization and the reaction kinetics. Our goal in this paper is to describe the kinetics of heterogeneous single-species annihilation, which is defined