Agenda
Friday 7 February 2020
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.
Paths, Groupoids and Quantization
Patrick Iglesias-Zemmour (HUJ, Israel)
I will show how, in the context of diffeology, one can find the prequatization framework for general diffeological spaces (finite or infinite dimensional, in presence of singularities or not) as a groupoid, quotient of the space of paths, equipped with a left-right invariant connectionlike-form. This construction suggests a variant of the program of geometric quantization which I will describe.