A spectral function for an interacting electron-lattice system

The lattice quasiparticle conserving Hamiltonian for an interacting electron-lattice system is employed in calculating the electromagnetic spectral response function in absorption for an electron located in a deep trap such that the electronic transition energies are much higher than the cutoff of the lattice vibrational spectrum. The zero-order Hamiltonian for the system is then diagonal in electronic quantum numbers and linear in the lattice vibrational mode coordinates. The spectral response is calculated for a dipole mediated transition by employing the temperature-dependent double-time Green's function technique. It is shown that because of the properties of the lattice field operators, the hierarchy of Green's function equations decouples and no higher-order Green's functions are required for obtaining an explicit solution to a given order. An exact solution for the absorption of spectrum in the lowest order in electromagnetic field is given in terms of delta-function lines. Broadening effects, numerical calculation restrictions and applications to molecular vibronic spectra are briefly discussed.