Alternating Kinetics of Annihilating Random Walks Near a Free Interface
Abstract
The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with alpha_n approximately equal to 0.225 for n=1 and all odd values of n; for all n even, a faster decay with alpha_n approximately equal to 0.865 is observed. From consideration of the eventual survival probability in a finite cluster of particles, the rigorous bound alpha_1<1/4 is derived, while a heuristic argument gives alpha_1 approximately equal to 3 sqrt{3}/8 = 0.2067.... Numerically, this latter value appears to be a stringent lower bound for alpha_1. The average position of the first particle moves to the right approximately as 1.7 t^{1/2}, with a relatively sharp and asymmetric probability distribution.
Keywords
Cite
@article{arxiv.cond-mat/9710252,
title = {Alternating Kinetics of Annihilating Random Walks Near a Free Interface},
author = {L. Frachebourg and P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/9710252},
year = {2009}
}
Comments
6 pages, RevTeX, 5 eps figures included