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Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation

Authors
  • Vernon, Daniel C.
Type
Published Article
Publication Date
Dec 22, 2003
Submission Date
Apr 16, 2003
Identifiers
DOI: 10.1103/PhysRevE.68.041103
arXiv ID: cond-mat/0304376
Source
arXiv
License
Unknown
External links

Abstract

A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the density of particles, and provides both an exact value for the exponent governing the decay of particles and an epsilon-expansion for the amplitude of this power law. When the diffusion is anomalous, as when the particles perform Levy flights, the critical dimension depends continuously on the control parameter for the Levy distribution. The epsilon-expansion can then become an expansion in a small parameter. We present a renormalization group calculation and compare these results with those of a simulation.

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