Long Range Hops in the A+A arrow ptyset Reaction: Renormalization Group and Simulation
Abstract
A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which may diffuse and annihilate in pairs. The renormalization group can be used to calculate the time dependence of the density of particles. Both an exact value for the exponent governing the decay of particles and an ɛ-expansion for the amplitude of this power law may be obtained. When the diffusion is anomalous, as when the particles perform Lévy flights, the critical dimension depends continuously on the control parameter for the Lévy distribution. The ɛ-expansion can then become an expansion in a small parameter. We present the renormalization group calculation and compare these results with those of a simulation.
- Publication:
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APS March Meeting Abstracts
- Pub Date:
- March 2003
- Bibcode:
- 2003APS..MARV15013V