Semiclassical phase space evolution of Fermi resonance spectra

Abstract

The evolution of the semiclassical phase space of a Fermi resonance spectrum is investigated as the strength of the resonance coupling is varied between zero and the strong coupling limit. The phase space evolution gives information beyond that contained in the phase space profile of the experimental spectrum alone. The zero-order phase space is found to be different in important respects from that of the pendulum model of a nonlinear resonance. In the weak coupling regime, the phase space evolution is essentially like that of a dynamical barrier picture. In the strong coupling regime of ‘‘intrinsic resonance,’’ the phase space structure is much different. Topology change appears to take place in a more discontinuous manner than in the weak coupling regime. The phase space evolution shows that some levels are problematic for an adiabatic switching treatment. The origin of some anomalous levels seen both in phase space profiles of experimental spectra and in semiclassical quantization studies is clarified.