Trivial resonances for a system of Klein-Gordon equations and statistical applications.

by Annalaura Stingo (Polytechnique)

Tuesday May 20, 2025, 2:00 PM → 3:00 PM Europe/Paris

Amphi Jordan. (ICJ)

In the derivation of the kinetic equation from the cubic NLS, a key feature is the invariance of the Schrödinger equation under the action of U(1), which allows the quasi-resonances of the equation to drive the effective dynamics of the correlations. In this talk, I will give an example of equation that does not enjoy such type of invariance and show that the exact resonances always take precedence over quasi-resonances. As a result, the effective dynamics is not of kinetic type but still nonlinear. I will present the problem, the ideas behind the derivation of the effective dynamics and some elements of the proof. This is based on a recent work in collaboration with de Suzzoni (École Polytechnique) and Touati (CNRS and Université de Bordeaux).