Vibrational Relaxation in a Localized Excited Electronic State by the GME Method

A theory of the time evolution of the vibrational state of the lattice following an instantaneous excitation of a localized electronic state is presented for a simple model permitting both, the formal exact (in the basis of the deformed lattice states) and the second order generalized master equation (GME) treatment. The Nakajima‐Zwanzig form of the GME is used. The resulting integro‐differential equations are solved exactly by the generating function method (novel in this context) and the physical contents of the solution are discussed.