What We Talk About When We Talk About Dissipative Quantum Chaos

TL;DR

This paper reviews recent developments in dissipative quantum chaos, a field extending quantum chaos concepts from closed to open quantum systems, with new tools for distinguishing and measuring chaos in such systems.

Contribution

It provides a comprehensive review of the foundational theories, recent progress, and experimental tests in dissipative quantum chaos.

Findings

Development of spectral analysis tools for open quantum systems.

Recent experimental validations of theoretical predictions.

Growth in research publications over the last decade.

Abstract

Dissipative quantum chaos is an emerging theory that is expected to extend the ideas, concepts, and methodology of conventional Hamiltonian quantum chaos from coherent evolution to open quantum dynamics. The new theory should provide a set of tools to distinguish chaotic open quantum systems from integrable ones, as well as quantitative measures of their chaoticity (or, conversely, integrability). The foundations of this theory were laid in the late 1980s, and from the very start it was clear that, like its Hamiltonian predecessor, it had to be based on the spectral properties of the operators governing open quantum evolution. After these first steps, the field remained relatively quiet for many years and it is only over the last decade that the development of dissipative quantum chaos has received a strong boost, as confirmed by a large number of publications on this topic and, very recently, the first experiments performed to test its theoretical predictions. In this chapter, we review these recent developments and outline the basic foundations of dissipative quantum chaos.