Numerical study of intramolecular vibrational energy transfer: Quantal, classical, and statistical behavior

The dynamics of a system of two coupled, one-dimensional, nonlinear oscillators is studied both quantum mechanically and classically. The quantal and classical dynamics substantially agree in most cases including some in which the maximal Lyapunov number indicates the classical behavior is stochastic. An exception occurs when one oscillator is prepared in a highly excited state. In such a case, the classical behavior is stochastic and significantly more ergodic than the quantal behavior. The source of the reduced quantal ergodicity is identified as failure of the classical approximation for narrow nonlinear resonances. Model calculations suggest that layers of reduced ergodicity similar to the one in the present system may be prevalent in real molecules. Quantal and classical statistical calculations are performed for comparison with the dynamical results. The quantal statistical calculations are based on a definition of quantal mixing which is discussed in some detail. The computed quantal statistics agree well with the corresponding classical statistics. However, the statistics do not agree very well with the dynamics for either the quantal or the classical case. The implications of these results for classical treatments of unimolecular dynamics, statistical intramolecular behavior, and the RRKM theory are discussed.