The Effect of Static Disorder and Reactant Segregation on the $A + B \to \emptyset$ Reaction

Abstract

We derive the long-time behavior of the ${A} + {B} \to \emptyset$ reaction in two dimensions, finding a universal exponent and prefactor in the absence of disorder. Sufficiently singular disorder leads to a (sub)diffusion-limited reaction and a continuously variable decay exponent. Pattern matching between the reactant segregation and the disorder is not strong enough to affect the long-time decay.