The Poincare-Birkhoff theorem in Quantum Mechanics

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.

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

References in corpus (7)

• Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
• Resonance-Assisted Tunneling
• Goos-Haenchen shift and localization of optical modes in deformed microcavities
• Dynamical tunneling in molecules: Quantum routes to energy flow
• Signatures of homoclinic motion in quantum chaos
• Scarring by homoclinic and heteroclinic orbits
• Selective amplification of scars in a chaotic optical fiber

Cited by in corpus (9)

• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• First-order quantum phase transitions: test ground for emergent chaoticity, regularity and persisting symmetries
• Observation of resonance-assisted dynamical tunneling in an asymmetric microcavity
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Fractal nature of high-order time crystal phases
• Universal wave functions structure in mixed systems
• Dynamical tunneling across the separatrix
• Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case
• Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard