Mathematics

We consider the semiclassical limit from the Hartree-Fock equation to the Vlasov equation with general singular interaction potentials, including the Coulomb and gravitational interactions. In these cases, the Vlasov equation models the time evolution of the density of a dense plasma and the dynamics of galaxies respectively. We will show that the convergence holds in the strong topologies of Schatten norms for a large class of initial data and provide explicit bounds (based on a joint work with L. Laflèche).