Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2020-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://www.epj-conferences.org/articles/epjconf/pdf/2020/02/epjconf_mmcp2019_02005.pdf |
| Summary: | 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. |
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| ISSN: | 2100-014X |