A Description of Quantum Chaos

TL;DR

This paper introduces a new measure called the entropic chaos degree for quantum dynamics, demonstrating its effectiveness in characterizing chaos in quantum systems like spin 1/2 models.

Contribution

It provides a novel definition of the entropic chaos degree for quantum transition dynamics and proves its validity in distinguishing chaotic from non-chaotic quantum systems.

Findings

Non-chaotic quantum dynamics have zero chaos degree.

The chaos degree accurately describes chaos in quantum spin systems.

The measure applies to dissipative and other quantum dynamics.

Abstract

A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.