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Branching and annihilating Lévy flights.

D Vernon1, M Howard

  • 1Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
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This study explores particle systems with branching and annihilation, revealing how Lévy flight behavior shifts critical transition points. Different particle movement patterns lead to distinct universality classes in absorbing-active phase transitions.

Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Complex Systems

Background:

  • Investigates particle systems with simultaneous branching (A-->(m+1)A) and annihilation (A+A-->Ø) reactions.
  • Incorporates long-range Lévy flights, where movement probability decays as r^(-d-sigma).

Purpose of the Study:

  • To analyze branching and annihilating Lévy flight systems using field theoretic renormalization group (RG) techniques.
  • To compare RG results with Monte Carlo simulations in one dimension (d=1).
  • To understand the impact of the Lévy flight parameter sigma on critical behavior and universality classes.

Main Methods:

  • Field theoretic renormalization group (RG) analysis near the upper critical dimension (d(c)=sigma).
  • Monte Carlo simulations in d=1.

Related Experiment Videos

  • Measurement of critical exponents as a function of sigma.

    • Main Results:

    • For sigma near 1 in d=1, the absorbing-active phase transition occurs at zero branching rate.
    • For sigma > 3/2 in d=1, the critical branching rate increases with sigma, indicating a different universality class.
    • This second universality class is inaccessible via controlled perturbative expansions.

    Conclusions:

    • The system exhibits distinct critical behaviors depending on the Lévy flight parameter sigma.
    • A transition between universality classes occurs around sigma ≈ 3/2 in d=1.
    • RG and simulations provide complementary insights into these complex non-equilibrium phenomena.