Dynamics of a dissipative two level system

We consider the tunneling of a particle in a symmetric double well, which is coupled to its environment in a way, that classically corresponds to a damping constant γ. In the two lowest level subspace, this is described by a spin-boson model with a finite density of zero energy excitations. A relaxation kernel method is applied to calculate the low temperature, low frequency static and dynamical susceptibility. In particular we determine the average tunneling frequency, which is equivalent to the rate for the destruction of phase coherence. For weak damping this is shown to be finite in the limit T→0, whereas for large γ it vanishes with a power low in T. At T=0 the two regimes are separated by a phase boundary, dividing regions with finite or zero effective tunnel splitting. We discuss the application of the model to the dynamics of flux states in SQUID's and also to paraelectric impurities.