Chaotic dynamics and approximate semiclassical quantization: Assigning highly excited vibrational eigenstates

Assigning the low lying vibronic states of CH3O and CD3O

The assignment of lines in vibrational spectra in strongly mixing systems is considered. Several low lying vibrational states of the ground electronic X∼²E state of the CH₃O and CD₃O radicals are assigned. Jahn-Teller, spin-orbit, and Fermi couplings mix the normal mode states. The mixing complicates the assignment of the infrared spectra using a zero-order normal mode representation. Alternative zero-order representations, which include specific Jahn-Teller couplings, are explored. These representations allow for definitive assignments. In many instances it is possible to plot the wavefunctions on which the assignments are based. The plots, which are shown in the adiabatic representation, allow one to visualize the effects of various higher order couplings. The plots also enable one to visualize the conical seam and its effect on the wavefunctions. The first and the second order Jahn-Teller couplings in the rocking motion dominate the spectral features in CH₃O, while first order and modulated first order couplings dominate the spectral features in CD₃O. The methods described here are general and can be applied to other Jahn-Teller systems.

Dynamics of a single ion in a perturbed Penning trap: octupolar perturbation

Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.