  We consider the quantum dynamics of $N$ interacting fermions in the large $N$
limit. The particles in the system interact with each other via repulsive
interaction that is regularized Coulomb potential with a polynomial cutoff with
respect to $N$.From the quantum system, we derive the Vlasov-Poisson system by
simultaneously estimating the semiclassical and mean-field residues in terms of
the Husimi measure.
