The Inhibition of Mixing in Chaotic Quantum Dynamics

TL;DR

This paper investigates how quantum interference effects can inhibit classical mixing in a chaotic quantum system, especially when the wave packet remains confined, leading to persistent amplitude on the potential barrier.

Contribution

It reveals a dynamic mechanism where quantum interference prevents mixing by pinning amplitude on the barrier, contrasting classical chaotic behavior.

Findings

Quantum behavior matches classical when confined within the separatrix.

Quantum interference causes long-lived amplitude accumulation on the barrier.

Inhibition of mixing occurs once classical motion becomes unbounded.

Abstract

We study the quantum chaotic dynamics of an initially well-localized wave packet in a cosine potential perturbed by an external time-dependent force. For our choice of initial condition and with $\hbar$ small but finite, we find that the wave packet behaves classically (meaning that the quantum behavior is indistinguishable from that of the analogous classical system) as long as the motion is confined to the interior of the remnant separatrix of the cosine potential. Once the classical motion becomes unbounded, however, we find that quantum interference effects dominate. This interference leads to a long-lived accumulation of quantum amplitude on top of the cosine barrier. This pinning of the amplitude on the barrier is a dynamic mechanism for the quantum inhibition of classical mixing.