Generalized Moyal structures in phase-space, master equations and their classical limit: II. Applications to harmonic oscillator models

The formalism of the phase-space representation of quantum master equations via generalized Wigner transformations developed in a previous paper, is applied to the Lindblad-type kinetic equation, for a quantum harmonic oscillator coupled to an equilibrium bath of oscillators. The resulting equation is derived without introducing the rotating-wave approximation. In the classical limit, the equation reduces to a Fokker–Planck equation, which coincides with the one derived from the corresponding classical Hamiltonian. The formalism is also applied to other oscillator model equations often used in quantum optics