On dynamical tunneling and classical resonances

Details On dynamical tunneling and classical resonances On dynamical tunneling and classical resonances

2007-07-29

arxiv.org/abs/0707.4274v1

J. Chem. Phys. vol 122, 114109 (2005)

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1063/1.1881152

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.

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