https://doi.org/10.1051/epjconf/202022602005
Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading
1
Pavol Jozef Šafárik University,
Šrobárova 2,
041 54
Košice,
Slovakia
2
Institute of Experimental Physics, Slovak Academy of Sciences,
Watsonova 47,
040 01
Košice,
Slovakia
3
Joint Institute for Nuclear Research,
141980
Dubna,
Russia
★ e-mail: sarlota.birnsteinova@student.upjs.sk
Published online: 20 January 2020
We study fluctuation effects in the two-species reaction-diffusion system A + B → Ø and A + A → (Ø, A). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays in d dimensions with the distance r according to a power-law r−d−σ. For anomalous diffusion (including Lévy flights) the critical dimension dc = σ depends on the control parameter σ, 0 < σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind the B particle density calculation.
© The Authors, published by EDP Sciences, 2020
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