Correlation-function analysis of nonlinear and nonadiabatic systems: Polaron tunneling

Signatures of nonlinearity and nonadiabaticity are studied in the context of small polarons through various correlation functions which measure structural and optical (absorption and fluorescence) properties of a system. It is shown that energy-resolved correlation functions can be used to probe length and time scales in a unique fashion. These methods are applied to a polaron-tunneling problem which not only serves as a prototype for nonlinear and nonadiabatic behavior but may also be relevant to describing aspects of local electronic and structural dynamics in high-${\mathit{T}}_{\mathit{c}}$ superconducting materials.