Decoding the Dynamical Information Embedded in Highly Excited Vibrational Eigenstates: State Space and Phase Space Viewpoints

Abstract

We study the nature of highly excited eigenstates of strongly coupled multimode systems with three degrees of freedom. Attempts to dynamically assign the eigenstates using classical-quantum correspondence techniques poses a considerable challenge, due to both the number of degrees of freedom and the extensive chaos in the underlying classical phase space. Nevertheless, we show that sequences of localized states interspersed between delocalized states can be identified readily by using the parametric variation technique proposed earlier by us. In addition, we introduce a novel method to lift the quantum eigenstates onto the classical resonance web using a wavelet-based local time-frequency approach. It is shown that the lifting procedure provides clear information on the various dominant nonlinear resonances that influence the eigenstates. Analyzing the spectroscopic Hamiltonians for CDBrClF and CF(3)CHFI as examples, we illustrate our approach and demonstrate the consistency between state space and phase space perspectives of the eigenstates. Two exemplary cases of highly mixed quantum states are discussed to highlight the difficulties associated with their assignment. In particular, we provide arguments to distinguish between the states in terms of their predominantly classical or quantum nature of the mixing.