The Transition Between Regular and Chaotic Dynamics and Its Influence on the Vibrational Energy Transfer in Molecules After Local Preparation

Abstract

AbstractThe classical as well as the quantum dynamics of two‐dimensional nonseparable oscillator systems is studied in order to investigate the influence of regular and chaotic motion on the nature of the intermode vibrational energy transfer after local excitation. Representative sets of initial conditions ‐ each element representing a single phase space cell — were chosen. For the classical problem one phase space point per cell was used while for the quantum problem minimum uncertainty wave packets (harmonic oscillator coherent states) with position and momentum expectation values corresponding to the classical values were taken as initial quantum states. For both types of motion information entropies were determined from time averaged probabilities. These entropies are compared with “ergodic limit entropies”. The latter correspond to a statistical preparation of the initial states. Although there is only a weak correspondence between single‐trajectory motion and wave packet dynamics, some general predictions about the quantum dynamics can be made from the classical results for a time scale of chemical interest. No sharp transition is found for the wave packet dynamics going from the classically regular to the irregular energy region. However, one can estimate the probability for an arbitrarily prepared local minimum uncertainty wave packet to possess statistical (RRKM) or non statistical (non‐RRKM) dynamics from the analysis of a sample of classical trajectories each starting in a phase space cell of the bound area of the Hamiltonian, i.e., the nature of unimolecular reactions can be roughly predicted from the potential energy surface and a sample group of classical trajectories.