TRANSPORT OF EXCITATION-ENERGY IN A 3-DIMENSIONAL DOPED MOLECULAR-CRYSTAL .4. 4TH-ORDER PROPAGATION, EXCITON CLOTHING, AND EXCITON DIFFUSION

The problem of excitons in interaction with phonons in a molecular cry stal has been reinvestigated as a continuation of our earlier work. Th e exciton-phonon interaction has been taken to be linear in lattice di splacements. The external medium, the phonon assembly, has been consid ered to be in thermal equilibrium. Following Simons, we have incorpora ted the effects of the medium on the exciton dynamics into a time-depe ndent effective potential that contains the equilibrium average excito n-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlatio n function that represents the probability of exciton transfer has bee n given in the interaction picture. The time evolution of this correla tion function has been determined by following Kubo's technique of cum ulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The seco nd- and fourth-order contributions have been diagrammatically represen ted. The second-order contribution has been explicitly calculated in d ifferent physical limits, namely, the slow exciton and the slow phonon limits at high and low temperatures and for very large and very small time. A few simple formulas for the transfer probability of a bare ex citon in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been spe cifically shown that the sum over phonon modes in the large time dynam ics leads to a fully destructive interference in second order at a ver y low temperature and gives rise to a diffusive transport at a high en ough temperature. A natural way of clothing the excitons has been cons idered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in term s of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of e xcitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attac hes a novel interpretation to the correlation function which was origi nally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physic al limits under the Debye model of phonon dispersion. From these resul ts a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. (C) 1996 John Wiley & Sons, Inc.