Exact Results for a Diffusion-Limited Pair Annihilation Process on a One-Dimensional Lattice

Abstract

The process of pair annihilation of particles diffusing on a ring of one-dimensional lattice is studied analytically. A set of master equations for the distribution functions of particles are solved exactly for the initial condition of uniform, random distribution of particles. An explicit expression for the time dependence of the density of particles is derived from the distribution functions. In the limit of infinite lattice, the present result agrees with the one obtained by [Balding, Clifford and Green: Phys. Lett. A 126 (1988) 481].