Breakdown of the quantum distinction of regular and chaotic classical dynamics in dissipative systems

The Grobe-Haake-Sommers (GHS) conjecture generalizes the Bohigas-Giannoni-Schmit conjecture to dissipative systems, connecting classically chaotic systems with quantum spectra that exhibit level repulsion as predicted by Ginibre ensembles. Here, we show that the GHS conjecture does not hold for the open Dicke model, which is a spin-boson model of experimental interest. Surprisingly, where the open quantum model shows Ginibre level statistics, we do not always find evidence of 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.