Dynamics of coupled spins in the white- and quantum-noise regime

We study the dynamics of dissipative spins for general spin-spin coupling. We investigate the population dynamics and relaxation of the purity in the white noise regime, in which exact results are available. Inter alia, we find distinct reduction of decoherence and slowdown of purity decay around degeneracy points. We also determine in analytic form the one-phonon exchange contribution to decoherence and relaxation in the ohmic quantum noise regime valid down to zero temperature.