Disorder-induced anomalous kinetics in the [formula presented] reaction

We address the two-dimensional bimolecular annihilation reaction [formula presented] in the presence of random impurities. Impurities with sufficiently long-ranged interactions are known to lead to anomalous diffusion, [formula presented], 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: [formula presented]. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.