Boundary effects in reaction-diffusion processes
Statistical Mechanics
2009-10-31 v1
Abstract
The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a doped TMMC crystal. We show that a density excess, which extends into the system diffusively from the boundary, is formed in two dimensions and below. This implies a surprising result for the magnetisation near a fixed spin in the coarsening of the one-dimensional critical Ising model. The universal, dimensionally-dependent functional forms of this density excess are given by an exact solution and the field-theoretic renormalisation group.
Keywords
Cite
@article{arxiv.cond-mat/9903009,
title = {Boundary effects in reaction-diffusion processes},
author = {M. J. E. Richardson and Y. Kafri},
journal= {arXiv preprint arXiv:cond-mat/9903009},
year = {2009}
}