Reaction-Subdiffusion Equations for the A <--> B Reaction

TL;DR

This paper models a reversible reaction under subdiffusion using CTRW, revealing that the reaction equations are coupled through transport operators of both reactants, due to multiple transitions at a single site before jumps.

Contribution

It introduces a novel mesoscopic reaction-subdiffusion system where the evolution of each reactant depends on both its own and the other's transport operators, due to subdiffusive behavior.

Findings

Reaction equations are coupled through Laplacian terms of both reactants.

Multiple A to B and B to A transitions occur at a single site before jumps.

The model captures the nonlocal effects of subdiffusion on reactions.

Abstract

We consider a simple linear reversible isomerization reaction A <--> B under subdiffusion described by continuous time random walks (CTRW). The reactants' transformations take place independently on the motion and are described by constant rates. We show that the form of the ensuing system of mesoscopic reaction-subdiffusion is somewhat unusual: the equation giving the time derivative of one reactant concentration, say A(x,t), contains the terms depending not only on Laplacian A, but also on Laplacian B, i.e. depends also on the transport operator of another reactant. Physically this is due to the fact that several transitions from A to B and back may take place at one site before the particle jumps.