The Vlasov equation for Coulomb systems and the Husimi picture


  • Membre de l'Institut Universitaire de France.


We explore the validity of the Vlasov equation as a semi-classical approximation of time-dependent Hartree-Fock and time-dependent LDA theories. We discuss the h → 0 limit for the propagation of quantal wavefunctions in terms of classical densities. The h → 0 limit is studied formally by means of its Wigner and Husimi phase-space representations. We consider an application to the valence electron cloud of metal clusters and show a comparison between quantal and Vlasov dynamics in this case.