Quantum dynamics of transitions in two-level electron–phonon systems with strong interactions

The Dyson equation and operators of nonorthogonal projection are used to calculate the frequency dependence of the relaxation coefficients of generalized kinetic equations for a two-level electron–phonon system. It is shown that the relaxation coefficients can be represented in the form of a continued fraction, the parameters of which can be expressed in terms of the Fourier transforms of the many-time correlation functions, these having a real physical meaning as the transition rates at the time $t$ in the second, fourth, etc., orders of perturbation theory. The fraction truncated at the first term in the corresponding limiting cases gives the representations well-known in the literature for the transition rate. The approach is generalized further to calculate the many-time correlation functions in the case of nonlinear electron–phonon coupling.