Invariant Tori, Effective Stability, and Quasimodes with Exponentially Small Error Terms II - ¶Birkhoff Normal Forms

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• 作者：G. Popov
• 刊名：Annales Henri Poincare
• 出版年：2000
• 出版时间：June 2000
• 年：2000
• 卷：1
• 期：2
• 页码：249-279
• 全文大小：559 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Dynamical Systems and Ergodic Theory
  Quantum Physics
  Mathematical Methods in Physics
  Relativity and Cosmology
  Elementary Particles and Quantum Field Theory
  
• 出版者：Birkh盲user Basel
• ISSN：1424-0661

文摘

. The aim of this paper is to obtain quasimodes for a Schrödinger type operator Ph in a semi-classical limit (h \searrow 0) (h \searrow 0) with exponentially small error terms which are associated with Gevrey families of KAM tori of its principal symbol H. To do this we construct a Gevrey quantum Birkhoff normal form of Ph around the union L \Lambda of the KAM tori starting from a suitable Birkhoff normal form of H around L \Lambda . As an application we prove sharp lower bounds for the number of resonances of Ph defined by complex scaling which are exponentially close to the real axis. Applications to the discrete spectrum are also obtained.