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

TL;DR

This paper investigates how static disorder and reactant segregation influence the long-time decay behavior of the A + B -> ∅ reaction in two dimensions, revealing universal and disorder-dependent decay exponents.

Contribution

It derives the asymptotic decay laws for the reaction, showing the impact of disorder on the decay exponent and demonstrating the robustness of segregation effects.

Findings

Universal decay exponent in absence of disorder

Disorder induces variable decay exponents

Segregation pattern matching does not alter long-time decay

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.