Generalised Master Equation for the Spin-Boson Hamiltonian by the Projection Operator Technique

Abstract

Starting from the von Neuman equation of quantum theoretical dynamics, by using the projection operator technique, we write the generalised master equation (GME) of the reduced statistical operator. By using this technique we find a series expansion of the memory kernel which allows, in principle, a treatment of the higher orders of approximation. By keeping only the first term of this expansion, which corresponds to the second order of the perturbation treatment, GME is applied, in the Markov approximation, to the spin boson Hamiltonian to describe the dynamics of the relevant pseudo-spin subsystem. In the secular and rotating wave approximations this dynamics is found to be described by the Bloch equations.