Abstract
The motion of an exciton in a translationally invariant exciton-phonon system is considered within the frame of the generalized Fulton-Gouterman (FG) transformation, which diagonalizes the coupled exciton-phonon Hamiltonian in the excitonic subspace and yields a set of exact equations for the purely oscillatory FG wave functions. An exact expression for the second moment of the local excitonic occupation numbers is presented in terms of the FG wave functions, for which two different sets of displaced phonon states are discussed. A numerical computation of the second moment characterizes the exciton motion as a coherent process. This result is also found in an improved calculation which is based on the application of the Goldberger-Adams relation. \textcopyright{} 1996 The American Physical Society.
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