On dynamical tunneling and classical resonances

Abstract

This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling and explicit forms of the dynamical barriers can be obtained only by identifying the key resonances. Relationship between the phase space viewpoint and the quantum mechanical superexchange approach is discussed in near-integrable and mixed regular-chaotic situations. For near-integrable systems with sufficient anharmonicity the effect of multiple resonances {\it i.e.,} resonance-assisted tunneling can be incorporated approximately. It is also argued that the, presumed, relation of avoided crossings to nonlinear resonances does not have to be invoked in order to understand dynamical tunneling. For molecules with low density of states the resonance-assisted mechanism is expected to be dominant.

Completely rewritten and expanded version of a previous submission physics/0410033. 14 pages and 10 figures

References in corpus (15)

• Discrete Breathers
• Electron transmission through molecules and molecular interfaces
• Ray and wave chaos in asymmetric resonant optical cavities
• Resonance-assisted tunneling in near-integrable systems
• Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard
• Resonance-Assisted Tunneling
• Complex Periodic Orbits and Tunnelling in Chaotic Potentials
• Dynamical Tunneling in Mixed Systems
• Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
• Tunneling And The Onset Of Chaos In A Driven Bistable System
• Ionization via Chaos Assisted Tunneling
• Signatures of chaotic tunnelling
• Tunneling rate fluctuations induced by non-linear resonances: a quantitative treatment based on semiclassical arguments
• Dynamical tunneling in molecules: role of the classical resonances and chaos
• Tunneling of quantum rotobreathers

Cited by in corpus (17)

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• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
• Observation of resonance-assisted dynamical tunneling in an asymmetric microcavity
• Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator
• Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
• Quantum breathers in capacitively coupled Josephson junctions: Correlations, number conservation, and entanglement
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Quantum dynamics of localized excitations in a symmetric trimer molecule
• Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
• Creating triple-NOON states with ultracold atoms via chaos-assisted tunneling
• Eigenstates of Thiophosgene Near the Dissociation Threshold -- Deviations From Ergodicity
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
• Bichromatically driven double well: parametric perspective of the strong-field control landscape reveals the influence of chaotic states
• Resonance-assisted tunneling in 4D normal-form Hamiltonians
• Dynamical tunneling across the separatrix
• Resonance- and Chaos-Assisted Tunneling
• Arnold web and dynamical tunneling in a four-site Bose-Hubbard model