From N-body Schrödinger to Vlasov equation with singular potentials

par Laurent Laflèche (UT, Austin)

mardi 6 avr. 2021, 14:00 → 15:00 Europe/Paris

In this talk I will present several techniques and concepts used in the context of the mean-field and the semiclassical limit allowing to go from the quantum  models to the classical mean-field equations of kinetic theory.
The N-body Schrödinger equation describes the motion of N interacting particles at the quantum scale. In the limit of large number of particles, one obtains a mean-field equation called the Hartree equation, and when the Planck constant h becomes negligible, the Vlasov equation.
To link these equations, one possibility is to understand the similarity of the models and study the quantum analogue of the properties of the Wasserstein distances and Sobolev norms. This allows to obtain propagation of a semiclassical notion of regularity independent of N and h and quantitative results about the limits when N goes to infinity and h to 0.