The Poincare-Birkhoff theorem in Quantum Mechanics
arXiv:1105.1461 · doi:10.1103/PhysRevE.84.026206
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.
arXiv comment5 pages, 3 figures, Full resolution figures available at http://www.df.uba.ar/users/wisniaki/publications.html
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- Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard