A+B→0 AND A+A→0 CHEMICAL REACTIONS UNDER ENHANCED DIFFUSION CONDITIONS THROUGH THOMPSON'S METHOD

Abstract

In this work we use Thompson's method to study both A+B→0 and A+A→0 reactions under anomalous diffusion regimes. We consider a general action encompassing the two kinds of reactions, by including a non-brownian (γ<2) superdiffusion mechanism, for instance, Levy-mixing. Such a kind of mechanism leads to a continuous mixing of the reactants, which homogenizes the system, thereby partially suppressing the fluctuations. We show that for [Formula: see text], the segregation disappears in d=3 in the A+B→0 reaction in agreement with previous results of Zumofen, Klafter and Shlesinger. This last result can be interpreted as the erosion of the segregation in d=3. In the A+A→0 reaction, the superdiffusion mechanism leads to the decreasing of the upper critical dimension (d c ). We also show that, at d c , we always obtain logarithmic corrections both for the reactant concentrate decays (<∊>) and for the reaction rates (<K>).