Anomalous Kinetics of a Multi-Species Reaction-Diffusion System: Effect of Random Velocity Fluctuations

Abstract: Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of kinetic rate equations is not sufficient and the effect of density fluctuations has to be properly taken into account. Our aim here is to analyze a particular multi-species reaction-diffusion system characterized by reactions $\textit{A} +\textit{A} \rightarrow (\emptyset, A),$ $\textit{A} +\textit{B} \rightarrow \textit{A}$ at and below its critical dimension $d_c = 2$. In particular, we investigate effect of thermal fluctuations on the reaction kinetics, which are generated by means of random velocity field modelled by a stochastic Navier-Stokes equations. Main theoretical tool employed is field-theoretic perturbative renormalization group. The analysis is performed to the first order of the perturbation scheme (one-loop approximation).