Low frequency, low temperature properties of the spin-boson problem

Low temperature and low frequency properties of a spin-boson model are investigated within a super operator and Liouville space formulation. The leading contributions are identified with the help of projection operators projecting onto the equilibrium state. The quantities of interest are expressed in terms of weighted bath propagators and static linear and nonlinear susceptibilities. In particular the generalized Shiba relation and Wilson ratio are recovered.