Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading

• Published in: EPJ Web of Conferences Vol. 226; p. 2005
• Main Authors: Birnšteinová, Šarlota, Hnatič, Michal, Lučivjanský, Tomáš
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Les Ulis EDP Sciences 2020
• Subjects: Diffusion effects; Particle density (concentration); Species diffusion; Variations
• ISSN: 2100-014X; 2101-6275; 2100-014X
• DOI: 10.1051/epjconf/202022602005

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
d
c
=
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.