Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum–classical correspondence in a K-system: as $\mathrm{\hslash }\to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.