Quantum correlations for a simple kicked system with mixed phase space

TL;DR

This paper explores the classical and quantum dynamics of a simple kicked system with mixed phase space, revealing similar sticking phenomena but with quantum modifications, using a modified Markov tree model.

Contribution

It introduces a quantum-aware modification of the Meiss--Ott Markov tree model to explain quantum sticking behavior in a mixed phase space system.

Findings

Classical correlation decay follows a power law near the chaotic region.

Quantum correlation decay also follows a power law but with a smaller exponent.

Modified Markov tree model accounts for quantum limitations on flux.

Abstract

We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss--Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.