Conservative Quantum

mean-field quantum diffusion models A. Arnold 1 and C. Sparber 2 We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dynamical semigroup. Key words: open quantum system, Lindblad operators, quantum dynamical semigroup, dissipative operators, density matrix, Hartree equatio