Boundary effects in reaction-diffusion processes

TL;DR

This paper investigates how boundaries influence reaction-diffusion systems, revealing a diffusive density excess near boundaries in low dimensions, with implications for magnetization in spin models, supported by exact solutions and renormalization group analysis.

Contribution

It provides an exact analytical description of boundary effects in reaction-diffusion processes, including a universal form of the density excess in low dimensions.

Findings

Density excess extends diffusively from the boundary in two dimensions and below.

Universal functional forms of the density excess are derived.

Implications for magnetization near fixed spins in the 1D Ising model.

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.