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

TL;DR

This paper investigates how random impurities with long-range interactions cause anomalous diffusion and reaction kinetics in a two-dimensional bimolecular annihilation process, revealing that disorder fundamentally alters the long-term behavior.

Contribution

It applies renormalization group theory to a field theoretic model to show disorder induces anomalous kinetics in the $A+A o ext{empty}$ reaction.

Findings

Impurities cause subdiffusive behavior with <r^2(t)> ~ t^{1-δ}.

Reaction kinetics follow c(t) ~ t^{δ-1} in the presence of disorder.

Disorder shifts the system into a regime with fundamentally altered long-time kinetics.

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, $<r^2(t)> \sim t^{1-\delta}$, 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: $c(t) \sim t^{\delta -1}$. This kinetics results because the disorder forces the system into the (sub)diffusion controlled regime, in which the kinetics must become anomalous.