On the Long Time Behavior of the Quantum Fokker-Planck equation
  We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispersion estimates in the cases were no equilibrium state exists. 
C. Sparber, J. A. Carrillo, J. Dolbeault, P. A. Markowich