Averaging in quantum stochastics: a soluble model with coloured noise
Marek Kuś, Kazimierz Rza̧żewski, J L van Hemmens · Journal of Physics A Mathematical and General · 1984
The authors calculate the average of the quantum-dynamical evolution operator of a harmonic oscillator linearly coupled to a stochastic field with Lorentzian line shape of arbitrary bandwidth (Ornstein-Uhlenbeck process). In so doing they develop some new techniques to cope with the non-commutativity of the boson operators. They also compare the exact results with van Kampen's second-order cumulant expansion and find that the agreement is good if the bandwith is large.