The Poincare-Birkhoff theorem in Quantum Mechanics

2011/05/07 by D. A. Wisniacki, M. Saraceno, F. J. Arranz +2 · 3 citations
Physics and Astronomy · #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.84.026206

5 pages, 3 figures, Full resolution figures available at http://www.df.uba.ar/users/wisniaki/publications.html

arxiv created 2011/05/07 · arxiv updated 2015/05/28

Abstract

Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincaré--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

Cited by

• Chaos and Quantum Tunneling
• Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case
• Quantum precursors to Kolmogorov-Arnold-Moser theorem in Floquet spin-J systems