Resolvent expansion of time-dependent solutions in spin-boson systems

In order to describe the dynamics of the spin-boson system in the one-mode case the transition-probability amplitude is analytically treated for general initial and final states. By transcription into the Bargmann space of the entire functions a second-order differential equation is obtained. The latter is solved by a resolvent expansion. The described method is subsequently transferred to the multi-mode case. The time-dependent quantum-statistical spin expectation value with given initial state of the reservoir is reduced to the transition-probability amplitudes of the whole system. Reduction to the spin system as relevant system leads to a sum over all occupation configurations of the reservoir, which cannot be explicitely evaluated. (orig./HSI)