Bootstrap Approach to Fitting Spectra of Molecules with Classically ChaoticDynamics

摘要

The existence of the transition to chaos in classical mechanics has heldtremendous interest for the field of molecular dynamics. Chaotic dynamics is thought to have ramifications for spectra of highly excited rotation-vibration states, for energy-transfer processes, and for controlled molecular excitation and chemical change. In this paper, we investigate the feasibility of detailed, level-by level fitting of unassignable spectra of molecules with Hamiltonians having strongly chaotic dynamics. Roughly speaking, chaos results in the loss of all approximate zero-order quantum numbers in the chaotic system. The individual levels of the spectrum are in this sense intrinsically unassignable. A breakdown of the usual approximate selection rules occurs. Fundamental questions then arise concerning the analysis of experimental spectra in the chaotic regime. One may ask whether it is possible to analyze molecular spectra in the chaotic regime with anything like the detail to which spectroscopists are accustomed for lower-lying states.