EXACT SOLUTION OF THE SMALL-POLARON PROBLEM IN INFINITE DIMENSIONS

The spectral function of a single electron coupled to Einstein phonons (Holstein model) is calculated exactly in the limit of large space di mensionality, for any coupling strength and phonon frequency. A self-c onsistent mapping onto an effective impurity model leads to the soluti on in terms of a continued-fraction expansion for the electron propaga tor at zero temperature. True self-trapping is obtained only for finit e bandwidth, such as the case of a Bethe lattice in infinite dimension s. It is shown that at intermediate coupling multiphonon resonances de velop, corresponding to polaron states. Only the lowest one has long l ifetime, and the polaron mass is calculated.