Dr. Jacky Chong, 北京大学

We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quantum moments for the Hartree-Fock equation with singular pair interaction potential of the form |x-y|-a, including the Coulomb interaction. Using these estimates, we obtain quantitative bounds on the distance between solutions of the manybody Schrodinger equation and solutions of the Hartree-Fock and the Vlasov equations in Schatten norms. For a, we obtain global-in-time results when N. In particular, it leads to the derivation of the Vlasov equation with singular potentials. For a 2 ( 12 ; 1], our results hold only on a small time scale, or with an N-dependent cuto. The talk is based on our recent works in [1, 2, 3]. This is a joint work with Laurent Laeche and Chiara Saffrio. The talk will be delivered in English and is meant for the general audience.