Survival in two-species reaction-diffusion system with Lévy flights: renormalization group treatment and numerical simulations

Abstract

Abstract We analyze the two-species reaction-diffusion system including trapping reaction A + B → A as well as coagulation/annihilation reactions A + A → ( A , 0 ) where particles of both species are performing Lévy flights with control parameter 0 < σ < 2 , known to lead to superdiffusive behavior. The density as well as the correlation function for target particles B in such systems are known to scale with nontrivial universal exponents at space dimension d ⩽ d c . Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension d c = σ . The numerical simulations in one-dimensional case are performed as well. The quantitative estimates for the decay exponent of the density of survived particles B are in a good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in superdiffusive regime is higher than that in a system with ordinary diffusion.