Centre de Physique Théorique


Mercredi 14 octobre 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.

16h00 – 17h00, Online

Polarization mechanism for chemotaxis and exact scaling exponent in assemblies of cells

Charlie Duclut (Max-Planck Institute, Dresden)

To self-organise into complex structures such as tissues and organs, individual cells need to interact. A generic mechanism for this interaction is a chemical signalling. The ability of an individual cell to follow a gradient of chemicals is called chemotaxis. Starting from a microscopic description of chemotactic cells, I will present a coarse-graining procedure to describe an assembly of such particles. This system exhibits a phase transition that I will then study using a dynamical renormalisation group approach. This analysis indicates the crucial role of a polarized chemotactic interaction, usually overlooked in phenomenological approaches. Finally, I will discuss an emergent symmetry of the model that allows us to compute scaling exponents exactly. In particular, we deduce a superdiffusive behavior of the particle density fluctuations in all physical dimensions.