# How Lagrangian states evolve into random waves

## Location

Zoom: Please email Jonathan Luk (jluk@stanford.edu) for Zoom link.

Friday, March 5, 2021 11:00 AM

Maxime Ingremeau (Université de Nice)

Abstract: In 1977, Berry conjectured that eigenfunctions of the Laplacian on manifolds of negative curvature behave, in the high-energy (or semiclassical) limit, as a random superposition of plane waves. This conjecture, central in quantum chaos, is still completely open.

In this talk, we will consider a much simpler situation. On a manifold of negative curvature, we will consider a Lagrangian state associated to a generic phase. We show that, when evolved during a long time by the Schrödinger equation, these functions do behave, in the semiclassical limit, as a random superposition of plane waves.