Can Wave Packet Revivals Occur in Chaotic Quantum Systems?

Abstract

The short time revivals of initially localized wave packets are well known in simple, closed, 1-degree-of-freedom (1D) systems. In 2D or higher, if the system is integrable or has exclusively periodic dynamics, a generalization is possible. If the dynamics are chaotic, revivals have not been previously seen and are, a priori, not expected. Nevertheless, we have found that some stretched wave packets in a chaotic system experience, very early, surprisingly large recurrences. We extend a semiclassical theory founded on summing over heteroclinic orbits to determine a set of necessary conditions. The most important one is an Einstein-Brillouin-Keller-like quantization of classical flux crossing the turnstile formed by the stable and unstable manifolds of the initial wave packet's underlying central orbit.