Fractal Weyl law for open quantum chaotic maps

• 成果类型: Article
• 署名作者: Nonnenmacher, Stephane; Sjoestrand, Johannes; Zworski, Maciej
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.179.1.3
• 发表日期: 2014
• 页码: 179-251
• 关键词: zeta-function; semiclassical resonances; scattering poles; Lower bounds; resolvent; GROWTH; number; SPACES; set

摘要

We study a semiclassical quantization of Poincare 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 includes the case of several convex (hard) obstacles satisfying a no-eclipse condition.