Vibrational Energy Flow: A State Space Approach

Gruebele, Martin

doi:10.1002/9780470141731.ch3

Cited by 77 publications

(31 citation statements)

References 185 publications

(170 reference statements)

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“…Nevertheless, we expect that vibrational energy transport dynamics in molecules may be diffusive even if the limit of strong mixing modeled by the GOE is not yet reached. This expectation is based on experience with local random matrix theory (LRMT) [19], which captures the diffusion in vibrational state space of a molecule even when the corresponding classical dynamics in phase space is not fully chaotic [66][67][68][69][70]. Similarly, we expect vibrational energy propagated by eigenmodes of the Hessian matrix may well exhibit diffusive dynamics even if the statistical properties of the eigenmodes do not coincide with those of the GOE.…”

Section: Discussionmentioning

confidence: 99%

Vibrational energy transport in molecules and the statistical properties of vibrational modes

Pandey

Leitner

2017

Chemical Physics

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Statistical properties of the eigenmodes computed for two molecules, dodecane and perfluorododecane, are examined and compared with predictions of random matrix theory. The eigenmode statistics of the heat carrying modes of perfluorododecane correspond to Porter-Thomas statistics, whereas those for dodecane do not. Vibrational energy transport in the two molecules is also computed and found to be diffusive in perfluorododecane but not in dodecane, consistent with recent experiments. The correspondence between eigenmode statistics and vibrational energy transport dynamics in molecules as well as thermalization in molecules are discussed.

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Section: Discussionmentioning

confidence: 99%

Vibrational energy transport in molecules and the statistical properties of vibrational modes

Pandey

Leitner

2017

Chemical Physics

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“…Insights into several aspects of the IVR dynamics have been obtained over the past few decades with novel experimental [24][25][26][27] and theoretical approaches [3,5,6,[28][29][30][31][32][33][34][35]. These studies have brought out the utility of approximately conserved quantities called polyads, emphasized the importance of local density of states coupled to the initial state of interest, and the crucial role * srihari@iitk.ac.in played by various anharmonic resonances at a given energy of interest.…”

Section: Introductionmentioning

confidence: 99%

Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization

Karmakar

Keshavamurthy

2018

J. Phys. Chem. A

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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.

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“…Above the transition, T (E) > 1, energy flows over all states of the energy shell. Schofield and Wolynes [56,57] have argued that energy flow in the vibrational state space both just above and well beyond the transition can be described by a random walk in quantum number space, a picture that has been supported by numerical calculations over a wide range of time scales [50,[58][59][60][61]. The state-to-state energy transfer rate can be estimated by LRMT.…”

Section: Quantum Localization In Interior Of the Vibrational State Spacementioning

confidence: 99%

“…For this reason, we refer to the theory as LRMT. Several reviews of LRMT have already appeared [18,50,51], which have summarized the important steps toward arriving at prediction of the quantum ergodicity transition, energy flow in quantum number space above the transition, and applications to unimolecular rate theory. Here our focus is the role of vibrational superexchange on energy flow from edge states to the interior of the vibrational state space.…”

Section: Quantum Localization In Interior Of the Vibrational State Spacementioning

confidence: 99%

Semiclassical Analysis of Multidimensional Barrier Tunneling

2011

Dynamical Tunneling

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Vibrational Energy Flow: A State Space Approach

Cited by 77 publications

References 185 publications

Vibrational energy transport in molecules and the statistical properties of vibrational modes

Vibrational energy transport in molecules and the statistical properties of vibrational modes

Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization

Semiclassical Analysis of Multidimensional Barrier Tunneling

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