Orateurs
Titres et résumés
Nalini Anantharaman Quantum ergodicity on graphs
Le résultat d'ergodicité quantique que nous
avons démontré avec Etienne Le Masson
ne vaut que pour de grands graphes
réguliers. J'avais annoncé l'an dernier avoir une
nouvelle preuve,
susceptible d'adaptation à des graphes plus généraux. Je décrirai
l'avancement des recherches dans cette direction et j'énoncerai un
résultat pour les marches
aléatoires anisotropes sur les graphes
réguliers.
Jean Marc Bouclet Wave packets on Riemannian manifolds
Frédéric Faure Asymptotic expression of the transfer operator for large times
Maxime Ingremeau Distorded plane waves in chaotic scattering
Distorded plane waves, also called Eisenstein functions, are a family of eigenfunctions
of a Schrödinger operator which are not square integrable. We will study the behaviour
in the semiclassical limit of distorded plane waves on manifolds that are euclidean near
infinity, under the assumption that the underlying classical dynamics has a hyperbolic
trapped set, and that some topological pressure is negative ; we will emphasize the case
of manifolds of nonpositive curvature.
Etienne Le Masson Quantum ergodicity and averaging operators on the sphere
Emmanuel Schenck Resonances near the real axis in chaotic scattering
We consider in this talk compact perturbations of the Laplacian on
manifolds Euclidian at infinity. If the classical trapped set is
hyperbolic, we will explain the fact that there exists a strip below
the real axis where number of resonances grows at least
almost-linearly. The context of this type of result will be recalled,
together with the main lines of the proof. Doing so we will also
explain how in odd dimensions, some topological pressure involving the
unstable Jacobian can be determined from the scattering poles only.
Masato Tsujii Spectrum of transfer operators for expanding semi-flows
Henrik Ueberschär Spectral geometry of tori with random impurities
An important object of study in the theory of disordered quantum systems are
Schrödinger operators with a random potential. In 1958, Anderson discovered that,
for sufficiently strong disorder, their eigenfunctions could be exponentially localized at
the bottom of the spectrum. A major question in the mathematical physics of disordered
systems considers the existence of a delocalization transition. I.e. if the disorder is
sufficiently weak compared with the energy, do there exist delocalized eigenfunctions?
I will address this question in the case of random delta potentials.