Comments on exciton phonon coupling: Temperature dependence

Abstract
We discuss upper bounds to the free energy of an excitoninteracting 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 a b r u p t transition from a delocalized to a localized exciton with an increase in temperature is discussed.