We discuss upper bounds to the free energy of an exciton interacting with a lattice of phonons with a linear coupling. From these upper bounds, we find the effective number of phonons clothing an exciton to vary with exciton bandwidth and temperature. The possibility of an abrupt transition from a delocalized to a localized exciton with an increase in temperature is discussed.
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Yarkony et al. (1976) studied this question.
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