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We implement continued-fraction techniques to solve exactly quantum masterequations for a spin with arbitrary S coupled to a (bosonic) thermal bath. Thefull spin density matrix is obtained, so that along with relaxation andthermoactivation, coherent dynamics is included (precession, tunnel, etc.). Themethod is applied to study isotropic spins and spins in a bistable anisotropypotential (superparamagnets). We present examples of static response, thedynamical susceptibility including the contribution of the different relaxationmodes, and of spin resonance in transverse fields.Comment: Resubmitted to J. Phys. A: Math. Gen. Some rewriting here and there.  Discussion on positivity in App.D3 at request of one refere

Solving spin quantum master equations with matrix continued-fraction methods: application to superparamagnets