Mixed dynamics from the classical and quantum ergodic hierarchy

TL;DR

This paper introduces a framework for analyzing mixed classical and quantum systems with both integrable and chaotic regions, linking phase space intuition to ergodic hierarchy levels, exemplified by the kicked rotator.

Contribution

It presents a novel formalism connecting mixed phase space features with ergodic hierarchy levels in classical and quantum systems.

Findings

Framework successfully describes mixed systems with integrable and chaotic regions.

Connects phase space intuition with ergodic hierarchy levels.

Illustrated with the kicked rotator example.

Abstract

Based on the classical and quantum ergodic hierarchy, a framework for mixed systems with a phase space composed by two uncorrelated integrable and chaotic regions is presented. It provides some features of mixed systems connecting the intuitive notion of a mixed phase space with the mixing level of the ergodic hierarchy. The formalism is illustrated with the kicked rotator.