Connection between approximate Fokker - Planck equations and the Wigner function applied to the micromaser
M. Elk, P. Lambropoulos · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · 1996
We present a derivation of a Fokker - Planck equation for the micromaser based on the Wigner function and valid in the semiclassical limit. The resulting equation is shown to correspond to the conventionally used approximate Fokker - Planck equations obtained for a continuous approximation to the discrete Fock representation of the density matrix of the light field. We thus establish a connection between the continuous approximation and the Wigner function. Then expressing expectation values as properly symmetrized products, we can extend in an exact way the validity of the Fokker - Planck approach to the micromaser down to the zero pump off-state of few photons and purely thermal statistics.