In these notes we review the material presented at the summer school on “Mathematical
Physics, Analysis and Stochastics” held at the University of Heidelberg in July 2014. We …

In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov
equation,(2) the classical limit of the N-body linear Schrödinger equation uniformly in N …

We study the many body Schrödinger evolution of weakly coupled fermions interacting
through a Coulomb potential. We are interested in a joint mean field and semiclassical …

We consider the evolution of quasi-free states describing N fermions in the mean field limit,
as governed by the nonlinear Hartree equation. In the limit of large N, we study the …

We introduce a new method for deriving the time-dependent Hartree or Hartree-Fock
equations as an effective mean-field dynamics from the microscopic Schrödinger equation …

We consider the semiclassical limit from the Hartree to the Vlasov equation with general
singular interaction potential including the Coulomb and gravitational interactions, and we …

I review results concerning the derivation of effective equations for the dynamics of
interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective …

In this paper, we prove a quantitative version of the semiclassical limit from the Hartree to the
Vlasov equation with singular interaction, including the Coulomb potential. To reach this …

In this paper, we define a quantum analogue of the notion of empirical measure in the
classical mechanics of N-particle systems. We establish an equation governing the evolution …

Using a new stability estimate for the difference of the square roots of two solutions of the
Vlasov $\unicode {x2013} $ Poisson equation, we obtain the convergence in the $ L^ 2 …