Theory of exciton transport in the limit of strong intersite coupling. I. Emergence of long-range transfer rates

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Abstract
A theory of exciton transport in molecular crystals is constructed by developing exact memory functions for pure systems and obtaining from the transfer rates for exciton motion which are particularly applicable in the limit of strong intersite coupling. This extension into the strong-coupling region is useful to stochastic-Liouville-equation theories as well as to the generalized-master-equation approach. Long-range transfer rates are shown to emerge from the analysis. They connect sites unconnected by matrix elements of the interaction and even the ordinary (Markoffian) rate equation used for the long-time description of exciton motion is thus shown to require modification for the strong-coupling case. Exact results are obtained for crystals of an arbitrary number of sites and particular cases of one-dimensional systems of a small number as well as an infinite number of sites are examined. Consequences of the new transport equations are obtainex explicitly by analyzing the moments of the probability distribution as well as the probabilities themselves, and the former are used to extend an earlier theory of unified rates to strong-coupling situations in extended systems. Applications of the theory to experiment are discussed. The theory is directly applicable to the transport of other quasiparticles, in particular to that of small polarons.