Transient A+B→0 reaction on fractals: stochastic and deterministic aspects

In this paper we study the transient diffusion-limited A+B→0, A₀ = B₀ annihilation via deterministic reaction-diffusion equations and via simulation of the stochastic many-particle problem. We show that the two approaches are not equivalent and that the deterministic expressions capture only part of the picture. A lower bound is derived for the density decay which indicates that the overall density follows the power law t^-x with α = mm(d/4, 1). Hierarchical oscillations superimposed on the power-law decay are observed for reactions on Sierpinski gaskets.