Disorder-Induced Anomalous Kinetics in the $A+A \to \emptyset$ Reaction

Abstract

We address the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of random impurities. Impurities with sufficiently long-ranged interaction energies are known to lead to anomalous diffusion, $<r^2(t)> \sim t^{1-δ}$, in the absence of reaction. Applying renormalization group theory to a field theoretic description of this reaction, we find that this disorder also leads to anomalous kinetics in the long time limit: $c(t) \sim t^{δ-1}$. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.