Relaxation in a dissipative two-level system: A projection operator approach

The projection operator technique previously developed by us is extended to the analysis of the time evolution of a dissipative two-level system when the tunnel splitting cannot be used as a perturbation parameter. After transforming the Hamiltonian, an interaction part can be identifies to carry out the calculations to second order in it. An approximate expression for the relaxation of the difference in the population of the localized states of the system is found and analyzed.