  We apply the Merrifield variational method to the Holstein molecular crystal
model in D dimensions to compute non-adiabatic polaron band energies and
Franck-Condon factors at general crystal momenta. We analyze these observable
properties to extract characteristic features related to polaron self-trapping
and potential experimental signatures. These results are combined with others
obtained by the Global-Local variational method in 1D to construct a polaron
phase diagram encompassing all degrees of adiabaticity and all electron-phonon
coupling strengths. The polaron phase diagram so constructed includes disjoint
regimes occupied by "small" polarons, "large" polarons, and a newly-defined
class of "compact" polarons, all mutually separated by an intermediate regime
occupied by transitional structures.

Materials Science;Superconductivity