Short time de-excitation dynamics of a two-level electron system. Non-perturbative solution of the master equation

A new general non-perturbative method for the solution of the generalized master equation for a simple two-level model of the electron-phonon system coupled to a thermodynamic reservoir is suggested. The model includes a two-level system interacting linearly with the single-mode phonons coupled to the thermodynamic bath. For the interaction of the bath with the vibrational mode we use a stochastic model generalized to finite temperatures. The results are compared with a direct numerical solution. (author)