Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading
Pavol Jozef Šafárik University,
2 Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
3 Joint Institute for Nuclear Research, 141980 Dubna, Russia
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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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