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

TL;DR

This paper investigates a two-species superdiffusive reaction system using renormalization group analysis and numerical simulations, revealing universal scaling exponents and higher survival probabilities compared to normal diffusion.

Contribution

It provides the first analytical calculation of scaling exponents for superdiffusive two-species reactions below the critical dimension, supported by numerical validation.

Findings

Analytical exponents match numerical results in 1D.

Superdiffusion increases target particle survival probability.

Scaling behavior is governed by nontrivial universal exponents.

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.