A master equation theory of excitonic annihilation phenomena for finite latices of low dimensionality

A master equation is written for the equation of motion for the vector p(t), in which the nth component corresponds to the probability of observing n excitons on a lattice with L sites. The dependence of the properties of p(t) on the magnitude of L, the intensity of excitation, the lattice dimensionality, and the magnitude of the biexcitonic annihilation rate is discussed. The dependence of the biexcitonic annihilation rate on the exciton density is discussed in the context of a simple simulation of exciton annihilation. The applicability of these ideas to excitonic annihilation in polymers is discussed.