Title: semiclassical limit from Hartree to Vlasov equation
Abstract: The Vlasov equation describes the evolution of a system of particles in interaction at a mesoscopic scale. Its counterpart in quantum mechanics is the Hartree equation and it can be proved that it converges in some sense to the Vlasov equation when the Planck constant $\hbar$ becomes negligible. In this talk, we will show how this convergence can be quantified by introducing the Wigner transform and semiclassical versions of the Wasserstein-Monge-Kantorovitch distance and the kinetic Lebesgue norms.