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arXiv · 2206.03947

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

Dmytro Shapoval·Viktoria Blavatska·Maxym Dudka
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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 L\'evy 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 $d \leq d_{c}$. 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.

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Dmytro Shapoval, Viktoria Blavatska, Maxym Dudka. 2022-06-08. Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations. https://doi.org/10.1088/1751-8121%2Fac9c39

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