Breakdown of the Quantum Distinction of Regular and Chaotic Classical Dynamics in Dissipative Systems

TL;DR

This paper challenges the universality of the GHS conjecture by showing that in the open Dicke model, spectral correlations do not always correspond to classical chaos, highlighting complexities in defining quantum chaos in dissipative systems.

Contribution

The study demonstrates that the GHS conjecture does not universally apply to dissipative quantum systems, specifically in the open Dicke model, questioning established links between classical chaos and quantum spectral properties.

Findings

Cubic level repulsion does not always indicate classical chaos in the open Dicke model.

The GHS conjecture's applicability is limited in dissipative quantum systems.

Spectral correlations in open quantum systems can arise independently of classical chaotic structures.

Abstract

Quantum chaos has recently received increasing attention due to its relationship with experimental and theoretical studies of nonequilibrium quantum dynamics, thermalization, and the scrambling of quantum information. In an isolated system, quantum chaos refers to properties of the spectrum that emerge when the classical counterpart of the system is chaotic. However, despite experimental progress leading to longer coherence times, interactions with an environment can never be neglected, which calls for a definition of quantum chaos in dissipative systems. Advances in this direction were brought by the Grobe-Haake-Sommers (GHS) conjecture, which connects chaos in a dissipative classical system with cubic repulsion of the eigenvalues of the quantum counterpart and regularity with linear level repulsion. Here, we show that the GHS conjecture does not hold for the open Dicke model, which is a spin-boson model of experimental interest. We show that the onset of cubic level repulsion in the open quantum model is not always related with chaotic structures in the classical limit. This result challenges the universality of the GHS conjecture and raises the question of what is the source of spectral correlations in open quantum systems.