Emergence of Gaussian fields in noisy quantum chaotic dynamics (Martin Vogel, Strasbourg)

23.10.2023 16:15 – 18:15

Abstract:
The theory of quantum chaos aims to describe quantum mechanical states in an environment where the classical dynamics is chaotic. The guiding example is the Laplace-Beltrami operator on a compact hyperbolic smooth manifold and it is conjectured by Rudnick and Sarnack that the underlying chaotic classical dynamics on such manifolds results in delocalization properties of the eigenfunctions of the Laplace-Beltrami operator. In this talk, we shall consider a toy model for this: we will show how Lagrangian states propagated by the semi-group induced by a suitable random Schrödinger operator converge locally to a stationary monochromatic isotropic Gaussian field.

This is joint work with M. Ingremeau.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Maths-Physique"

entrée libre