Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath

We study the reduced dynamics of interacting spins, each coupled to its own bath of bosons. We derive the solution in analytic form in the white-noise limit and analyze the rich behaviors in diverse limits ranging from weak coupling and) or low temperature to strong coupling and) or high temperature. We also view the single spin as being coupled to a spin-boson environment and consider the regimes in which it is effectively nonlinear and in which it can be regarded as a resonant bosonic environment.