2003/04/30 by Daniel C. Vernon, Daniel Vernon
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.68.041103
published as Phys. Rev. E vol 68 article 041103 (2003) · As-published version; two significant errors fixed, two references added
openalex publication_date 2003/10/10 · arxiv created 2003/12/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A simple example of a nonequilibrium 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 Lévy flights, the critical dimension depends continuously on the control parameter for the Lévy distribution. The epsilon 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.