We first review the usefulness of the Wigner distribution functions (WDFs), associated with Lindblad and pre-master equations, for analysing a host of problems in quantum optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation as a starting-point: (a) use of a reduced WDF but in the context of an exact master equation (b) use of a WDF for the complete system corresponding to entanglement at all times.
Publication Source (Journal or Book title)
Journal of Optics B: Quantum and Semiclassical Optics
O'Connell, R. (2003). Wigner distribution function approach to dissipative problems in quantum mechanics with emphasis on decoherence and measurement theory. Journal of Optics B: Quantum and Semiclassical Optics, 5 (3) https://doi.org/10.1088/1464-4266/5/3/369