Based on the projection operator technique we provide a new method to describe the dissipative two state system dynamics, that we name resonance treatment. In parallel, the same problem is reviewed from the path-integral perspective. Basic concepts of the quantum dissipation are reviewed for both methods, the path-integral formalism and projection operator technique. Mathematically, the evolution of the reduced statistical operator is considered. The generalised master equation written in the framework of the projection operator technique exhibits a Redfield form. By applying it to the spin-boson Hamiltonian in the simplified case of secular and rotating wave approximations, we find Bloch-type equations describing the dynamics of the reduced statistical operator. The transversal and longitudinal relaxation times and the frequency bath-induced shift of the natural frequency (in absence of the bath) of the two-state system are calculated. The spectroscopist law having, as reported in the literature, a positive pure dephasing rate constant is obtained. The dynamics found by the resonance treatment is compared with that found by the path-integral formalism. The dissipative TSS dynamics found by the resonance treatment, in limit of secular and rotating wave approximations is applied to certain electron transfer reactions, namely in the case of the relative weak coupling between reactants and environment.
Buy this Article