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Application of Resonance Perturbation Theory to Dynamics of Magnetization in Spin Systems Interacting with Local and Collective Bosonic Reservoirs

We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions for the evolution of the reduced density matrix elements. This allows us to calculate explicitly the dynamics of the macroscopic magnetization, including characteristic relaxation and dephasing time-scales. We demonstrate that collective effects (i) do not influence the character of the relaxation processes but merely renormalize the relaxation times, and (ii) significantly modify the dephasing times, leading in some cases to a complicated (time inhomogeneous) dynamics of the transverse magnetization, governed by an effective time-dependent magnetic field.