Quantum mechanics of a classically chaotic system: Observations on scars, periodic orbits, and vibrational adiabaticity

Abstract

We present a detailed study of the classical and quantum mechanics of a strongly chaotic quartic oscillator. The topology of the motion is such that there is a channel in which one has good separation of time scales. Many quantum states are found to scar along these channels. An adiabatic breakup for the action of the periodic orbits based on adiabatic stability of orbits is used to derive an approximate, integrable Hamiltonian. Semiclassical quantization of this Hamiltonian yields accurate energies for all states scarred along the channels.