The Reaction Process A+A->O in Sinai Disorder

TL;DR

This paper investigates how Sinai disorder affects the reaction A+A->O in diffusion processes, revealing that weak disorder can increase reaction rates in two dimensions, while stronger disorder causes sub-diffusion limitations below two dimensions.

Contribution

It introduces a field-theoretic analysis of the A+A->O reaction in Sinai disorder, showing how disorder influences reaction rates and diffusion limitations across dimensions.

Findings

Weak Sinai disorder increases reaction rate in two dimensions.

Disorder causes sub-diffusion limitations below two dimensions.

Universal behavior of density when expressed in disorder-averaged diffusion length.

Abstract

The single-species reaction-diffusion process $A+A\to O$ is examined in the presence of an uncorrelated, quenched random velocity field. Utilising a field-theoretic approach, we find that in two dimensions and below the density decay is altered from the case of purely diffusing reactants. In two-dimensions the density amplitude is reduced in the presence of weak disorder, yielding the interesting result that Sinai disorder can cause reactions to occur at an {\it increased} rate. This is in contrast to the case of long-range correlated disorder, where it was shown that the reaction becomes sub-diffusion limited. However, when written in terms of the microscopic diffusion constant it is seen that increasing the disorder has the effect of reducing the rate of the reaction. Below two dimensions, the effect of Sinai disorder is much more severe and the reaction is shown to become sub-diffusion limited. Although there is no universal amplitude for the time-dependence of the density, it is universal when expressed in terms of the disorder-averaged diffusion length. The appropriate amplitude is calculated to one-loop order.