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

TL;DR

This paper explores how classical and quantum mechanisms, especially near resonance junctions on the Arnold web, influence intramolecular vibrational energy redistribution, highlighting the transition from coherent to incoherent dynamical tunneling and eigenstate delocalization.

Contribution

It demonstrates that quantum IVR dynamics near resonance junctions can be predicted from classical Arnold web structures and identifies quantum signatures of eigenstate delocalization at these junctions.

Findings

Classical chaos influences quantum IVR pathways.

Transition from coherent to incoherent tunneling with increased coupling.

Eigenstates near junctions are delocalized due to dynamical tunneling.

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.