STRUCTURES IN CLASSICAL PHASE-SPACE AND QUANTUM CHAOTIC DYNAMICS

We compare the quantum and classical dynamics of a particle moving in a cosine potential while subject to a time-dependent force. We concent rate here on the behavior of an initially well-localized wave packet a t times before the classically chaotic motion is fully developed. We f ind that the quantum and classical dynamics are indistinguishable well beyond the Ehrenfest time where the wave packet delocalizes. The quan tum and classical descriptions first differ precisely when the classic al probability density is folded in the vicinity of a hyperbolic fixed point. At this point, the wave function acquires a nodal structure wh ich we show to be the result of a simple beating phenomenon between pa ths in the semiclassical propagator.