Intramolecular vibrational energy redistribution from a high frequency mode in the presence of an internal rotor: Classical thick-layer diffusion and quantum localization

We study the effect of an internal rotor on the classical and quantum intramolecular vibrational energy redistribution (IVR) dynamics of a model system with three degrees of freedom. The system is based on a Hamiltonian proposed by Martens and Reinhardt (J. Chem. Phys. {\bf 93}, 5621 (1990).) to study IVR in the excited electronic state of para-fluorotoluene. We explicitly construct the state space and show, confirming the mechanism proposed by Martens and Reinhardt, that an excited high frequency mode relaxes via diffusion along a thick layer of chaos created by the low frequency-rotor interactions. However, the corresponding quantum dynamics exhibits no appreciable relaxation of the high frequency mode. We attribute the quantum suppression of the classical thick-layer diffusion to the rotor selection rules and, possibly, dynamical localization effects.Comment: To appear in J. Chem. Phys. (August 28, 2007); 4 pages and 3 figure

Resonance-assisted tunneling in three degrees of freedom without discrete symmetry

We study dynamical tunneling in a near-integrable Hamiltonian with three degrees of freedom. The model Hamiltonian does not have any discrete symmetry. Despite this lack of symmetry we show that the mixing of near-degenerate quantum states is due to dynamical tunneling mediated by the nonlinear resonances in the classical phase space. Identifying the key resonances allows us to suppress the dynamical tunneling via the addition of weak counter-resonant terms.Comment: 4 pages, 4 figures (low resolution

On dynamical tunneling and classical resonances

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