IMPRS Seminar: Semiclassical Localization of Eigenmodes and Metastable States

Date

May 15, 2019

Time

1:00 PM - 2:00 PM

Speaker

Stéphane Nonnenmacher

Affiliation

Université Paris-sud

Series

IMPRS-MPSSE Seminar

Language

en

Main Topic

Physik

Other Topics

Physik

Description

One aspect of Quantum Chaos consists in studying the spectrum and eigenmodes of the Laplacian on a Euclidean billiard, or more generally on a Riemannian manifold, taking into account the paticular shape of the billiard/manifold. In absence of explicit formulas, one can nevertheless derive quantitative properties in the high frequency/semiclassical regime, where the geodesic flow becomes relevant. I will focus on the $L^2$ distribution of the eigenmodes across the manifold, and its lifts to phase space described by Wigner and Husimi functions. In the semiclassical limit, these functions converge to semiclassical measures, which are probability measures invariant by the geodesic flow. We aim at classifying those limiting measures, depending on the dynamical properties of the geodesic flow. I will mention some results about these semiclassical measures, in particular when the geodesic flow is chaotic. The same ideas/questions/methods have been applied to discrete time quantized dynamics on a compact phase space (say the 2-dimensional torus). I will also describe the situation of open systems, e.g. scattering by obstacles, for which eigenmodes are replaced by metastable states associated with complex valued resonances.

Last modified: Jun 24, 2019, 3:24:43 PM