Trivial resonances for a system of Klein-Gordon equations and statistical applications
Vortrag von Prof. Dr. Annalaura Stingo
Sprecher eingeladen von: Prof. Dr. Klaus Widmayer
Datum: 03.04.25 Zeit: 16.15 - 18.00 Raum: Y27H46
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 and non-trivial. 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 soon-to-appear work in collaboration with de Suzzoni (Ecole Polytechnique) and Touati (CNRS and Université de Bordeaux).