A+B→0 ENHANCED DIFFUSION-CONTROLLED REACTIONS UNDER STATIONARY REGIME CONDITION THROUGH THOMPSON'S APPROACH

Abstract

In this work, Thompson's method is used to study the A+B→0 reactions controlled by anomalous and brownian diffusion in the case of an external homogeneous source (h) of particles A and B under sthequiometric condition (the same input rate h) and also in the special case of the stationary regime. So the novelty in the present work is that we are able to obtain for such kind of reactions (σ=1) the static critical exponent δ of concentration [Formula: see text], the dynamical exponent for the relaxation time Δ'(τh~h-Δ') and the exponent for the concentration decaying ξ(∊~τ-ξ), with all these quantities evaluated in the limit h→0 (zero-field-rate). We also get scaling relations among new critical indexes. After we go further by obtaining more general results for such exponents so that we are able to include also the case of A+A→0(A) reactions within an unified scheme as already made before by introducing a general effective action (Aσ,γ). Thus, when we consider the case σ=0 (A,+A→0(A) reactions) we recover those critical exponents (δ,Δ',ξ) for anomalous coalescence reactions of type kA→lA(l<k). And when we even make γ=2 (brownian diffusion) we get the exponents previously given by Rácz, and also some results obtained by Lee and Oliveira. Thompson's method is a simple alternative way to the renormalization group scheme and has been shown to be a good description for long-time regime.