A theory of the kinematics of quasiparticle annihilation in lattices is developed on the basis of an exact calculation. Details relevant to its application to the annihilation of Frenkel excitons in molecular crystals are presented. Explicit expressions for observables such as the quantum yield and the time-dependent fluorescence intensity are obtained for one-, two-, and three-dimensional crystals. The range of validity of earlier theories is examined in the light of the exact solutions, and the limit of fast transport as well as that of fast annihilation is obtained. The effect of transport coherence is studied, and it is indicated how one might measure exciton coherence from the observables.

• Received 17 March 1980

DOI:https://doi.org/10.1103/PhysRevB.22.2089