Quantum ergodicity for time-dependent wave-packet dynamics

Abstract

The dynamics of nonstationary wave packets in model quantum-mechanical systems are studied for the properties of ergodicity and instability. The long-time-average Wigner phase-space distribution is calculated for each wave packet and analyzed for uniformity on a surface of section. A mild transition from nonergodic to ergodic behavior is observed with increasing energy. These results are compared to long-time averages of the wave-function probability density. The "stability" of each packet is also analyzed by several methods, including the "survival" of the initial state and a new measure of "separation" of similar wave packets. The relationships between the wave-packet ergodicity and instability and the corresponding classical dynamics are developed. Comparisons to other quantum-ergodic studies, and implications for intramolecular energy transfer and classical-ergodic studies are discussed.