Around Quantum Chaos (18w5002)


(McGill University)

Stéphane Nonnenmacher (Université Paris-Saclay)

(Northwestern university)


The Banff International Research Station will host the "Around Quantum Chaos (in conjunction with 2018 ICMP in Montreal)" workshop from July 15th to July 20th, 2018.

Quantum Chaos lies at the intersection of geometric analysis, PDE and mathematical physics, studying spectra and eigenstates of quantum systems, and relate them to the properties of the corresponding classical dynamical system, as predicted by the correspondence principle in quantum mechanics. Questions considered in QC include semiclassical correspondence between spectra and eigenfunctions of the Laplacian and the properties of the corresponding geodesic flows, as well as related results for billiard flows (as well as branching billiard flows), frame flows and other systems; spectra and eigenstates of graphs and quantum graphs; quantum scattering theory. There are strong connections to mathematical physics, PDE, quantum chemsitry, as well as to data analysis (manifold learning).

The workshop will gather specialists studying such problems for various systems, including Riemannian manifolds (with ergodic, completely integrable or mixed geodesic flows), arithmetic manifolds, quantum graphs, as well as random systems. The spectral theory of such systems is studied using a variety of different methods, including microlocal analysis, number theory, the theory of elliptic PDE, probabilistic methods and graph theory. The goal of the workshop is to review the latest progress in the field, and to facilitate interactions between specialists of different subdomains.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).