Mean Field Asymptotics of Generalized Quantum Kinetic Equation

We construct the mean field asymptotics of a solution of an initial value problem of the generalized quantum kinetic equation. As a result we rigorously derive the Vlasov quantum kinetic equation and the nonlinear Schrödinger equation. Moreover, the mean field asymptotics of a sequence of explicitly defined functionals of a solution of the generalized quantum kinetic equation, by which the average values of the nonadditive-type marginal observables are determined, is established. The obtained results are extended to particles interacting via many-body potentials.