N-level system in contact with a singular reservoir

We study a model of an N-level atom coupled linearly to an infinite free boson bath whose time correlation functions are Gaussian. We prove that, in the limit when the decay time of the correlations of the bath goes to zero, the reduced dynamics of the atom is given by a completely positive dynamical semigroup. By varying the interaction parameters, any such semigroup can be obtained in the limit. We also discuss the formally analogous situation of an N-level atom whose Hamiltonian contains an external fluctuating Gaussian stationary contribution.