From the Hartree equation to the Vlasov-Poisson system: strong convergence for a class of mixed states

Abstract

We consider the evolution of $N$ fermions interacting through a Coulomb or gravitational potential in the mean-field limit as governed by the nonlinear Hartree equation with Coulomb or gravitational interaction. In the limit of large $N$, we study the convergence in trace norm towards the classical Vlasov-Poisson equation for a special class of mixed quasi-free states.

21 pages. Typos corrected, references updated and detailed proof of Lemma 2.4 added