Branching annihilating Lévy flights: Irreversible phase transitions with long-range exchanges

1996 ◽  
Vol 34 (2) ◽  
pp. 97-102 ◽  
Author(s):  
E. V Albano
Keyword(s):  
Phase Transitions ◽  
Long Range ◽  
Lévy Flights ◽  
Levy Flights ◽  
Irreversible Phase Transitions

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

2020 ◽  
Vol 226 ◽  
pp. 02005
Author(s):  
Šarlota Birnšteinová ◽  
Michal Hnatič ◽  
Tomáš Lučivjanský
Keyword(s):  
Long Range ◽  
Anomalous Diffusion ◽  
Particle Density ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Group Method ◽  
Theoretic Approach ◽  
Lévy Flights ◽  
Levy Flights

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.

scholarly journals Survival probability of random walks and Lévy flights on a semi-infinite line

2017 ◽  
Vol 50 (46) ◽  
pp. 465002 ◽  
Author(s):  
Satya N Majumdar ◽  
Philippe Mounaix ◽  
Grégory Schehr
Keyword(s):  
Random Walks ◽  
Survival Probability ◽  
Lévy Flights ◽  
Levy Flights ◽  
Infinite Line

scholarly journals First Order Transition for the Optimal Search Time of Lévy Flights with Resetting

2014 ◽  
Vol 113 (22) ◽  
Author(s):  
Lukasz Kusmierz ◽  
Satya N. Majumdar ◽  
Sanjib Sabhapandit ◽  
Grégory Schehr
Keyword(s):  
Search Time ◽  
Order Transition ◽  
Optimal Search ◽  
Lévy Flights ◽  
First Order ◽  
Levy Flights ◽  
First Order Transition
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