Quantum Lyapunov exponents and complex spacing ratios: two measures of Dissipative Quantum Chaos

TL;DR

This paper compares two methods for classifying dissipative quantum systems as chaotic or regular, using spectral properties and Lyapunov exponents, and finds they generally agree in their categorizations.

Contribution

It relates spectral and Lyapunov-based approaches to dissipative quantum chaos, demonstrating their consistency across different quantum models.

Findings

Spectral and Lyapunov methods generally agree in classifying quantum chaos.

The study uses two quantum models to establish the relationship between approaches.

The work advances the toolbox for categorizing open quantum systems.

Abstract

The agenda of Dissipative Quantum Chaos is to create a toolbox which would allow us to categorize open quantum systems into "chaotic" and "regular" ones. Two approaches to this categorization have been proposed recently. One of them is based on spectral properties of generators of open quantum evolution. The other one utilizes the concept of Lyapunov exponents to analyze quantum trajectories obtained by unraveling this evolution. By using two quantum models, we relate the two approaches and try to understand whether there is an agreement between the corresponding categorizations. Our answer is affirmative.