Coherence properties of the stochastic oscillator

An oscillator with stochastic frequency is discussed as a model for evaluating the quantum coherence properties of a physical system. It is found that the choice of jump statistics has to be considered with care if unphysical consequences are to be avoided. We investigate one such model, evaluate the damping it causes, the decoherence rate and the correlations it results in and the properties of the state for asymptotically long times. Also the choice of initial state is discussed and its effect on the time evolution of the correlations.