Investigation of Ergodic Character of Quantized Vibrational Motion

The concept of quantum ergodicity and the degree of ergodic behavior reflected by the bound energy eigenstates are studied for some vibrational systems in two and three dimensions. Different approaches are attempted in order to be able to classify and quantify ergodicity in a given system by investigating the energy eigenfunctions. It is argued that the concept of quantum ergodicity is fundamentally connected to the similarity between eigenstates close in energy and to their globality. Previous investigations and definitions of quantum ergodicity can be seen to connect to this theme; they provide different measures of similarity between eigenstates. Here we propose two practical measures to investigate quantum ergodicity. The systems treated include the famous two-dimensional Henon-Heiles and Barbanis systems, which have previously been investigated both classically and quantum mechanically. As a more realistic three-dimensional example, we consider the vibrations of nonrotating NO 2 close to dissociation.