Quantum-classical correspondence and quantum chaos in the periodically kicked pendulum

The behavior of the periodically kicked pendulum is determined classically and quantum mechanically. Our earlier analytic study [Phys. Rev. A 41, 2952 (1990)] is confirmed and extended by the numerical results presented here. We are able to construct minimum uncertainty, Gaussian wave packets that maintain their form, and shadow the corresponding classical motion for long times when the classical motion is nonchaotic or only weakly chaotic. However, when the classical motion is robustly chaotic, the quantum-mechanical probability distribution grows macroscopically broad exponentially fast and the quantum-classical correspondence breaks down.