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arXiv · 1105.1461

The Poincare-Birkhoff theorem in Quantum Mechanics

D. A. Wisniacki·M. Saraceno·F. J. Arranz·R. M. Benito·F. Borondo
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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.

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D. A. Wisniacki, M. Saraceno, F. J. Arranz, R. M. Benito, F. Borondo. 2011-05-07. The Poincare-Birkhoff theorem in Quantum Mechanics. https://doi.org/10.1103/physreve.84.026206

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