Avoided crossings, scars, and transition to chaos

Abstract

The correlation diagram of the LiNC/LiCN isomerizing system as a function of ℏ, taken as a parameter, is considered in conditions of widespread classical chaos. Two series of isolated avoided crossings of very different nature, involving states related by the same 1:8 quantum resonance condition, are characterized and the corresponding interaction matrix elements between adiabatic states analytically calculated and analyzed. One of these series has been found to separate two distinct regions: one for smaller values of ℏ (at any given energy) corresponding to regular states, i.e., with a definite nodal pattern, and the other of much more stochastic behavior. Moreover, the effect of the interaction involved in these avoided crossings is to mix the regular wave functions giving rise to wave functions strongly scarred by the periodic orbits of the associated 1:8 classical resonance. This result constitutes an interpretation of the scarring effect from a new perspective. © 1997 American Institute of Physics.