Classical limit for linear and nonlinear quantum Fokker-Planck systems

We study the classical limit of some linear and nonlinear Quantum Fokker-Planck systems. In the nonlinear case we consider an Hartree-type potential. By the use of the Wigner transform and compactness methods, we prove the convergence of the system to a linear and nonlinear Vlasov Fokker- Planck equation respectively. The physical case with a Poisson coupling in three dimensions is included.