Quantum Optimal Transport, Sobolev Inequalities and Applications to Semiclassical Mean-field Limit
Time: 2023-08-16
Published By: He Liu
Speaker(s): Laurent Lafleche (Institut Camille Jordan, Université Claude Bernard Lyon 1, France)
Time: 10:00-11:00 August 18, 2023
Venue: Room 78201, Jingchunyuan 78, BICMR
A famous open problem in kinetic theory concerns the derivation of the Vlasov--Poisson equation from microscopic laws, the difficulty being the singularity of the interaction potential. In this context, it is possible to look at the joint mean-field and semiclassical limits, that is the limit from the $N$-body Schrödinger equation to the Hartree--Fock and Vlasov equations. As a first step, it is often useful to obtain regularity properties uniform in the Planck constant and the number of particles. It is therefore important to obtain analogous tools and inequalities in the context of quantum mechanics, such as operator versions of Wasserstein, Lebesgue and Sobolev distances. I will present these tools and their applications to the derivation of the Vlasov equation with singular potentials.
