Eigenstates of Thiophosgene Near the Dissociation Threshold -- Deviations From Ergodicity

A subset of the highly excited eigenstates of thiophosgene (SCCl$_{2}$) near the dissociation threshold are analyzed using sensitive measures of quantum ergodicity. We find several localized eigenstates, suggesting that the intramolecular vibrational energy flow dynamics is nonstatistical even at such high levels of excitations. The results are consistent with recent observations of sharp spectral features in the stimulated emission spectra of SCCl$_{2}$Comment: Accepted manuscript in The Journal of Physical Chemistry A, 10 pages,4 figure

Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization

In this work we study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction classical chaos is inevitably present and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates in order to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.Comment: 17 pages, 9 figures (reduced size), Accepted in J. Phys. Chem. A (2018) for William P. Reinhardt Festschrif

Driven coupled Morse oscillators --- visualizing the phase space and characterizing the transport

Recent experimental and theoretical studies indicate that intramolecular energy redistribution (IVR) is nonstatistical on intermediate timescales even in fairly large molecules. Therefore, it is interesting to revisit the the old topic of IVR versus quantum control and one expects that a classical-quantum perspective is appropriate to gain valuable insights into the issue. However, understanding classical phase space transport in driven systems is a prerequisite for such a correspondence based approach and is a challenging task for systems with more then two degrees of freedom. In this work we undertake a detailed study of the classical dynamics of a minimal model system - two kinetically coupled coupled Morse oscillators in the presence of a monochromatic laser field. Using the technique of wavelet transforms a representation of the high dimensional phase space, the resonance network or Arnold web, is constructed and analysed. The key structures in phase space which regulate the dissociation dynamics are identified. Furthermore, we show that the web is nonuniform with the classical dynamics exhibiting extensive stickiness, resulting in anomalous transport. Our work also shows that pairwise irrational barriers might be crucial even in higher dimensional systems.Comment: 10 pages, 5 figures. Contribution to William H. Miller festschrif

Dynamical tunneling in molecules: role of the classical resonances and chaos

In this letter we study dynamical tunneling in highly excited symmetric molecules. The role of classical phase space structures like resonances and chaos on the tunneling splittings are illustrated using the water molecule as an example. It is argued that the enhancements in the splittings due to resonances (near-integrable phase space) and due to chaos (mixed phase space) are best understood away from the fluctuations associated with avoided crossings. In particular we provide an essential difference between the two mechanisms in terms of high order perturbation theory. The analysis, apart from testing the validity of a perturbative approach, suggests such systems as prime candidates for studying dynamical tunneling.Comment: 4 pages, 3 figures (submitted to Phys. Rev. Lett.

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

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

Bichromatically driven double well: parametric perspective of the strong-field control landscape reveals the influence of chaotic states

The aim of this work is to understand the influence of chaotic states in control problems involving strong fields. Towards this end, we numerically construct and study the strong field control landscape of a bichromatically driven double well. A novel measure based on correlating the overlap intensities between Floquet states and an initial phase space coherent state with the parametric motion of the quasienergies is used to construct and interpret the landscape features. "Walls" of no control, robust under variations of the relative phase between the fields, are seen on the control landscape and associated with multilevel interactions involving chaotic Floquet states.Comment: 9 pages and 6 figures. Rewritten and expanded version of arXiv:0707.4547 [nlin.CD]. Accepted for publication in J. Chem. Phys. (2008