Quantum generalized Vlasov equation

An electronic system is considered as a quantum plasma characterized by a plasma parameter γ0 1, over short times. Using the Dynamics of Correlations (a many-body theory based on the Liouville-von Neumann equation in the Fourier transform of the Wigner-Weyl representation), in first and second order, a generalized Vlasov equation (GVE) has been derived. GVE describes as a particular situation the STLS (Singwi, Tosi, Land and Sjölander) ansatz. Discarding correlation terms in GVE, a non-linear Vlasov equation with exchange terms is derived. The classical limit and the linearization of GVE are also studied.