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

N. U. Nazarov, O. A. Ponomarev


Abstract: 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.

Received: 11.03.1990

 English version: Theoretical and Mathematical Physics, 1990, 85:1, 1072–1081

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