A. Isar et al., PHASE-SPACE REPRESENTATION FOR OPEN QUANTUM-SYSTEMS WITHIN THE LINDBLAD THEORY, International journal of modern physics b, 10(22), 1996, pp. 2767-2779
The Lindblad master equation for an open quantum system with a Hamilto
nian containing an arbitrary potential is written as an equation for t
he Wigner distribution function in the phase space representation. The
time derivative of this function is given by a sum of three parts: th
e classical one, the quantum corrections and the contribution due to t
he opening of the system. In the particular case of a harmonic oscilla
tor, quantum corrections do not exist.