Quantum ergodicity and vibrational relaxation in isolated molecules. II. λ-independent effects and relaxation to the asymptotic limit

Abstract

In this second article on quantum ergodic properties of simple anharmonic molecular models, we present further numerical calculations for the Barbanis and Henon‐Heiles models. For the cases studied herein, the density of energy eigenstates is larger by about a factor of five than that used earlier. We show that the character of the low lying states of the model Hamiltonians is dominated by λ‐independent effects which can be obtained by second order degenerate perturbation theory. Nondegenerate modifications of the above systems are again found to be highly nonergodic. We also discuss estimates of the time scale upon which the dynamics takes place. Two simple estimates are obtained on the basis of the ergodic properties and found to be reasonably accurate for the Barbanis system.