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Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visulaizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos., Comment: 12 pages, 6 figures (reduced size); Supplementary material can be accessed from the Journal site

We present the quantum and classical study of a four-well trapped Bose-Einstein condensate (BEC) modeled by the Bose-Hubbard Hamiltonian. The model used is fashioned as a minimal bipartite system consisting of a trimer coupled weakly to a monomer. Semiclassical insights into the fragmentation dynamics of the condensate is obtained by mapping out the Arnold web of the high dimensional classical phase space. A remarkable one-to-one correspondence between the quantum state space in occupation number representation and the classical Arnold web in action space is observed. The relevance of dynamical tunneling for the dynamics of Fock states near resonance junctions on the Arnold web is highlighted. We also predict the possibility of manipulating the transport within the trimer subsystem due to the weak coupling to the monomer., Comment: 14 pages 8 figures; Modified as per referee suggestions; Accepted in Physica D special issue on Chaos indicators

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 Festschrift

Intramolecular vibrational energy redistribution (IVR) impacts the dynamics of reactions in a profound way. Theoretical and experimental studies are increasingly indicating that accounting for the finite rate of energy flow is critical for uncovering the correct reaction mechanisms and calculating accurate rates. This requires an explicit understanding of the influence and interplay of the various anharmonic (Fermi) resonances that lead to the coupling of the vibrational modes. In this regard, the local random matrix theory (LRMT) and the related Bose-statistics triangle rule (BSTR) model have emerged as a powerful and predictive quantum theories for IVR. In this Perspective we highlight the close correspondence between LRMT and the classical phase space perspective on IVR, primarily using model Hamiltonians with three degrees of freedom. Our purpose for this is threefold. First, this clearly brings out the extent to which IVR pathways are essentially classical, and hence crucial towards attempts to control IVR. Second, given that LRMT and BSTR are designed to be applicable for large molecules, the exquisite correspondence observed even for small molecules allows for insights into the quantum ergodicity transition. Third, we showcase the power of modern nonlinear dynamics methods in analysing high dimensional phase spaces, thereby extending the deep insights into IVR that were earlier gained for systems with effectively two degrees of freedom. We begin with a brief overview of recent examples where IVR plays an important role and conclude by mentioning the outstanding problems and the potential connections to issues of interest in other fields., Comment: Accepted Phys. Chem. Chem. Phys Perspective article, 36 pages, 15 figures (reduced size)