Centre de Physique Théorique


Tuesday 18 February 2020

14h00 – 15h00, online-for link write to Annalisa Panati

Semiclassical limit from the Hartree equation to the Vlasov-Poisson system

Chiara Saffirio, Université de Basel, Suisse

The derivation of the Vlasov-Poisson equation, that describes the evolution of a systems of N interacting non-collisional particles at macroscopic scale, is a classical problem in mathematical physics. In this talk we will review this topic in the quantum setting, by using the Hartree equation as a bridge between the N-body Schrödinger equation and the Vlasov-Poisson system. We will show that a solution of the Hartree equation converges strongly towards a solution of the Vlasov-Poisson equation in the semiclassical limit.
The results hold for singular interactions (included the Coulomb and gravitational potentials) and exhibit explicit bounds on the convergence rate.