Phase Space Representation for Open Quantum Systems within the Lindblad   Theory
  The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this function is given by a sum of three parts: the classical one, the quantum corrections and the contribution due to the opening of the system. In the particular case of a harmonic oscillator, quantum corrections do not exist. 
A. Isar, A. Sandulescu and W.Scheid