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

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

2003-04-16

arxiv.org/abs/cond-mat/0304376v2

Phys. Rev. E vol 68 article 041103 (2003)

Physics

Condensed Matter

Statistical Mechanics

As-published version; two significant errors fixed, two references added

Scientific paper

10.1103/PhysRevE.68.041103

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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