Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations

Abstract

We analyze the two-species reaction-diffusion system including trapping reaction $A+B\to A$ as well as coagulation/annihilation reactions $A+A\to (A,0)$ where particles of both species are performing Lévy flights with control parameter $0<\sigma <2$, known to lead to superdiffusive behaviour. 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 $d\le d_c$. Applying the renormalization group formalism we calculate these exponents in a case of superdiffusion below the critical dimension $d_c=\sigma$. 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 good agreement with our analytical results. In particular, it is found that the surviving probability of the target particles in a superdiffusive regime is higher than that in a system with ordinary diffusion.

24 pages, 11 figures

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Cited by in corpus (2)

• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Two-species reaction-diffusion system in the presence of random velocity fluctuations