Study of molecular phase space structure through families of periodic orbits

Abstract

A systematic method to study the molecular phase space structure is presented by using a 2D potential function. The method includes the location of the principal families of periodic orbits as well as families which bifurcate from them and families of periodic orbits which are not associated with the principal families (irregular). The periodic orbits assist to calculate quantum low- and high-resolution spectra and to extract eigenfunctions by solving the time-dependent Schrödinger equation. For the studied system it is found that quantum states remain localized in chaotic phase space and show topological similarities with the periodic orbits. An explanation of this localization is sought by investigating the conjecture which requires the size of the turnstiles of a resonance to be less than Planck's constant. It is found that this conjecture fails for the type of eigenfunctions characterized by an irregular family of periodic orbits.