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

Abstract

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.

Arnold web and dynamical tunneling in a four-site Bose-Hubbard model

“…The origins for such behaviour has to do with the phenomenon of CAT [33,48,49] and RAT [32,49,50] in the vicinity of the multiplicity-2 resonance junctions and has been brought out clearly in earlier works [34,39,51] on different model systems. Near a resonance junction one expects a competition between transport due to local classical chaos and quantum transport dressed due to dynamical tunneling among near-degenerate states.…”

“…Since the Arnold web is a network of nonlinear resonances, one expects on rather general grounds that the phenomenon of resonance-assisted [32] and chaos-assisted [33] tunneling (RAT and CAT) will also be sensitive to the features on the web. In particular, due to the substantial degeneracy of the quantum states near the junctions one can have enhanced quantum transport due to the availability of multiple pathways [34][35][36]. Therefore, combined with the fact that chaotic dynamics occurs in the vicinity of the junctions, there is an intriguing possibility of subtle competition between the classical and quantum transport.…”

“…Therefore, combined with the fact that chaotic dynamics occurs in the vicinity of the junctions, there is an intriguing possibility of subtle competition between the classical and quantum transport. Note that recent studies [34,[37][38][39] in the molecular context have started to make progress on unraveling the influence of the junctions on both the classical and quantum transport. Thus, the multiple well trapped BECs provide a possible paradigm to experimentally identify these interesting higher dimensional transport and novel stability regimes.…”

Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians

“…Dynamical tunneling and specifically resonanceassisted tunneling has also been studied in higherdimensional systems [51][52][53][54][55]. Generically in such systems resonances of higher rank arise, which are not present in 2d systems.…”

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

“…Our results highlight specific features in the phase space, called as resonance junctions, that bring out the crucial role of the third degree of freedom in the transition to statisticality. Although hints about the role of the junctions to the IVR process have been around for nearly three decades [34][35][36][37][38][39][40][41][42][43][44], up until now there has been no effort to ascertain their importance in reaction dynamics. Here we precisely achieve this by explicitly correlating the dynamics near the resonance junctions with unimolecular dissociation lifetime distributions.…”