The Poincare-Birkhoff theorem in Quantum Mechanics

Details The Poincare-Birkhoff theorem in Quantum Mechanics The Poincare-Birkhoff theorem in Quantum Mechanics

2011-05-07

arxiv.org/abs/1105.1461v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--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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