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Notes: The problem of excitons in interaction with phonons in a molecular crystal has been reinvestigated as a continuation of our earlier work. The exciton-phonon interaction has been taken to be linear in lattice displacements. The external medium, the phonon assembly, has been considered to be in thermal equilibrium. Following Simons, we have incorporated the effects of the medium on the exciton dynamics into a time-dependent effective potential that contains the equilibrium average exciton-phonon interaction as well as terms arising from the fluctuations in the medium's coordinates about their equilibrium values. A correlation function that represents the probability of exciton transfer has been given in the interaction picture. The time evolution of this correlation function has been determined by following Kubo's technique of cumulant expansion. The zeroth-, second-, and fourth-order contributions to the correlation function have been calculated in this way. The second- and fourth-order contributions have been diagrammatically represented. The second-order contribution has been explicitly calculated in different 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 exciton in a molecular crystal of cubic symmetry have been derived from the Debye approximation for the dispersion of phonons. It has been specifically shown that the sum over phonon modes in the large time dynamics leads to a fully destructive interference in second order at a very low temperature and gives rise to a diffusive transport at a high enough temperature. A natural way of clothing the excitons has been considered and the clothed exciton has been represented diagrammatically. The dressing requires the correlation function to be redefined in terms of the clothed states and the clothed operators. The clothed exciton correlation function that represents the probability of transfer of excitons fully clothed by the phonons in thermal equilibrium turns out to be identical with the bare exciton correlation function. This attaches a novel interpretation to the correlation function which was originally defined by Simons. Transfer probabilities for a clothed exciton in a cubic crystal has been explicitly worked out for different physical limits under the Debye model of phonon dispersion. From these results a few expressions for the macroscopic diffusion coefficient of the clothed exciton have been obtained. A few critical comments have been incorporated. © 1996 John Wiley & Sons, Inc.