CHAOS AND THE CORRESPONDENCE LIMIT IN THE PERIODICALLY KICKED PENDULUM

The correspondence limit is illustrated for the periodically kicked pendulum. The classical dynamics of this system can be represented by a discrete map. A corresponding quantum map is derived and then rendered in the Ehrenfest formulation for expectation values. The Ehrenfest representation is studied for a minimum uncertainty Gaussian wave packet. It is shown that as Latin small letter h with stroke gets very small, followed by a decrease in the variance of the wave packet, the quantum map shadows the classical map with an error approaching zero for a length of time approaching infinity. The Gaussian form of the wave packet is preserved by the time evolution provided 0T 1. This constraint implies that the classical map is predominantly not chaotic with very small regions of very weak chaos. As 0T approaches 1, where the classical map becomes strongly chaotic, the propagation in time of the Gaussian wave packet completely breaks down. The possible significance of this breakdown is discussed. © 1990 The American Physical Society.