2005/03/15 by Srihari Keshavamurthy · 27 citations
Computer Science · Physics and Astronomy · #Anharmonicity #Chaotic #Classical mechanics #Computer science #Integrable system #Mathematical physics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Phase space #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Quantum tunnelling #Resonance (particle physics) #Space (punctuation) #Superexchange #nlin.CD
paper · pdf · doi:10.1063/1.1881152
published in The Journal of Chemical Physics 122(11), 114109 (American Institute of Physics) · Completely rewritten and expanded version of a previous submission physics/0410033. 14 pages and 10 figures
openalex publication_date 2005/03/15 · arxiv created 2007/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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, 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.