Quantum systems subject to the action of classical stochastic fields

In this paper we investigate the averaged dynamics of quantum systems under the influence of classical stochastic fields. This influence is modeled using a stochastic Hamiltonian evolution for the system-density matrix. From the averaged dynamics, a general characterization of the short-time decoherence behavior is obtained. General applicable short-time perturbation expansions for the input-output fidelity and its generalizations for mixed states are developed. The master equations of the systems that can be worked out without a perturbative expansion, i.e.. any system subject to dispersive noise and the quantum harmonic oscillator subject to amplitude noise, are extensively analyzed. In both cases all non-Markovian features are worked out in an exact way. We apply these cases to the study of heating of trapped ions.