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

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 → Ø at and below its critical dimension dc = 2. We use the second-quantization formalism of Doi to bring the stochastic problem to a field theory form. We investigate the reaction in spaces of dimension d ∼ 2 using a two-parameter expansion in ε and Δ, where ε is the deviation from the Kolmogorov scaling parameter and Δ 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.