New method for treating relaxation processes: Damped harmonic oscillator and the Jaynes-Cummings model with cavity losses

In the present paper a new technique for treating relaxation processes, based on the author's self-consistent projection-operator method, is developed. This nerv technique, which yields (instead of a master equation for a reduced density operator) equations of motion for probability amplitudes for a reduced set of states of the total system, opens a new way for treating relaxation processes. The applicability of the new method is demonstrated in the case of a damped harmonic oscillator and in that of the Jaynes-Cummings model with cavity losses.