Fractal Weyl law for open quantum chaotic maps
Analysis of PDEs
2011-05-17 v1 Dynamical Systems
Chaotic Dynamics
Abstract
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Cite
@article{arxiv.1105.3128,
title = {Fractal Weyl law for open quantum chaotic maps},
author = {Stéphane Nonnenmacher and Johannes Sjoestrand and Maciej Zworski},
journal= {arXiv preprint arXiv:1105.3128},
year = {2011}
}
Comments
69 pages, 7 figures