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

TL;DR

This paper investigates the decay dynamics of diffusing and annihilating particles using renormalization group methods, including anomalous diffusion via Levy flights, and compares theoretical predictions with simulation results.

Contribution

It applies renormalization group analysis to a non-equilibrium particle system with pair annihilation, extending to anomalous diffusion and validating results through simulations.

Findings

Exact decay exponent for particle density obtained

Epsilon-expansion for amplitude derived

Agreement between RG calculations and simulations

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.