Maxime Ingremeau (Université Côte d'Azur)

Quantum chaos under generic perturbations

Abstract:

Quantum chaos is the study of Laplace eigenfunctions (or more generally, of the propagation of waves) in geometries where the classical dynamics is chaotic. After presenting several open problems in quantum chaos, I will explain how one can obtain new results when a small (pseudodifferential) random perturbation is added to the Laplacian. Specifically, I will present two kinds of results: one comparing the evolution of Lagrangian states with Gaussian fields, in the spirit of Berry’s random wave model; the other, giving improved L^∞ bounds on the eigenfunctions. This is joint work with Martin Vogel.