Study of anomalous kinetics of the annihilation reaction A + A → Ø

Abstract

Using the perturbative renormalization group, we study the influence of a random velocity field on the kinetics of the single-species annihilation reaction A+A->0 at and below its critical dimension d_c=2. We use the second-quantization formalism of Doi to bring the stochastic problem to a field-theoretic form. We investigate the reaction in the vicinity of the space dimension d=2 using a two-parameter expansion in $\epsilon$ and $\Delta$, where $\epsilon$ is the deviation from the Kolmogorov scaling parameter and $\Delta$ is the deviation from the space dimension d=2. We evaluate all the necessary quantities, including fixed points with their regions of stability, up to the second order of the perturbation theory.