Quantum and classical descriptions of position and phase-space densities of a model Hamiltonian

Abstract

Excited states of a model Hamiltonian with strongly coupled modes are investigated. Comparisons are made between the classical Poincaré surfaces of section and the Husimi function, which is a quantum mechanical phase-space density function. It is found that for the majority of states the Husimi function exhibits local maxima which resemble in shape and location the invariant tori of Poincaré surfaces of section. For certain anomalous states the maxima in the Husimi function bears no such resemblance, and these states are considered as quantum chaotic.