Chiara Saffirio - From the Many-Body Quantum Dynamics to the Vlasov Equation

Explore a lecture on the derivation of the Vlasov equation from many-body quantum dynamics. Delve into the joint mean-field and semiclassical limit of N-body Schrödinger dynamics, covering both classical and quantum particles. Examine the Hartree-Fock theory for interacting fermions as a bridge between many-body and Vlasov dynamics. Learn about singular interactions, convergence rates, and the state of the art in this field. Investigate topics such as the Weyl and Wigner transforms, Grönwall type estimates, and the Fefferman-de la Llave representation formula. Gain insights into kinetic theory models for charged or gravitating particles through this comprehensive 52-minute presentation by Chiara Saffirio at the Hausdorff Center for Mathematics.

Intro
Derivation from N-particle system
Classical particles: mean-field regime
Classical particles: state of the art
Quantum particles: fermionic mean-field regime
Fermionic thean-field regime
Effective equation
State of art
Semiclassical limit
Weyl and Wigner transforms
Grönwall type estimate
Fefferman - de la Llave representation formula
Estimate on the dominant term
Remarks