Spectral representations for the time correlation functions of noninvariant systems in the theory of nonadiabatic transitions

The probabilities of vibronic transitions are represented, after elimination of the electron variables, in terms of the time correlation functions of the vibrational subsystem, which is noninvariant with respect to time shifts due to its interaction with the electron subsystem. For the noninvariant vibrational subsystem, a connection is established between the spectral intensities of the correlation functions and the retarded Green's functions; in the harmonic approximation, this connection can be found by solving a singular integral equation. In the framework of the phenomenological approach in which the retarded Green's function of the free vibrational subsystem is assumed to be known, the established connection makes it possible to investigate the influence of mode coupling on the kinetic and spectral characteristics of the system. Some special cases in which the integral equation admits exact solution are considered.