Dynamical ordering: Applications to Fokker-Planck equations
Arkadiusz Orłowski, Krzysztof Wódkiewicz · Physical Review A · 1994
A transformation of the linear second-order Fokker-Planck equations occurring in quantum optics is presented which overcomes difficulties connected with negative definiteness of the diffusion matrices. This transformation is based on a dynamical ordering of quantum quasiprobability distribution functions. The ordering depends on the parameters of the dynamical problem under consideration. An algorithm leading to exact solutions of the dynamically ordered Fokker-Planck equations with arbitrary initial conditions is given, and simple criteria, how to recognize squeezed light in arbitrary ordering, are presented. The problem of Fokker-Planck equations with time-dependent diffusion is also investigated.