Erwin Schrödinger Institute, Vienna, Austria
This summer school will present the research field of "quantum chaos" to an audience of graduate students, postdocs and young researchers. It is organized by Nalini Anantharaman (Orsay), Stéphane Nonnenmacher (Saclay), Zeév Rudnick (Tel-Aviv) and Steve Zelditch (Northwestern).
The aim of this field is to understand the dynamics of quantum (or wave) systems admitting a chaotic classical counterpart. One is especially interested in a precise description of the eigenvalues and eigenmodes of the quantum Hamiltonian of such a system. A paradigmatic example is the wave (or Schrödinger) equation on a compact Riemannian manifold of negative curvature, for which the quantum Hamiltonian is the Laplace Beltrami operator.
The school will consist of several basic courses (elementary dynamical systems theory, semiclassical analysis, random matrices and random waves) which will introduce the subject to the students and other participants. They will be followed by more advanced talks presenting some spectacular recent progress.
The school is supported by the European Mathematical Society, the International Association of Mathematical Physics and the Erwin Schrödinger Institute, where it will take place. It will also benefit from some funding from the National Science Foundation.