Geodesic
Quantum dynamics of~transitions in~two-level electron--phonon systems with strong interactions
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 89-101

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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. 
@article{TMF_1990_85_1_a8,
     author = {N. U. Nazarov and O. A. Ponomarev},
     title = {Quantum dynamics of~transitions in~two-level electron--phonon systems with strong interactions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {89--101},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a8/}
}
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N. U. Nazarov; O. A. Ponomarev. Quantum dynamics of~transitions in~two-level electron--phonon systems with strong interactions. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 89-101. http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a8/