Transient and steady-state chaos in dissipative quantum systems
Abstract
Dissipative quantum chaos plays a central role in the characterization and control of information scrambling, non-unitary evolution, and thermalization, but it still lacks a precise definition. The Grobe-Haake-Sommers conjecture, which links Ginibre level repulsion to classical chaotic dynamics, was recently shown to fail [Phys. Rev. Lett. 133, 240404 (2024)]. We properly restore the quantum-classical correspondence through a dynamical approach based on entanglement entropy and out-of-time-order correlators (OTOCs), which reveal signatures of chaos beyond spectral statistics. Focusing on the open anisotropic Dicke model, we identify two distinct regimes: transient chaos, marked by rapid early-time growth of entanglement and OTOCs followed by low saturation values, and steady-state chaos, characterized by high long-time values. We introduce a random matrix toy model and show that Ginibre spectral statistics signals short-time chaos rather than steady-state chaos. Our results establish entanglement dynamics and OTOCs as reliable diagnostics of dissipative quantum chaos across different timescales.
Cite
@article{arxiv.2506.05475,
title = {Transient and steady-state chaos in dissipative quantum systems},
author = {Debabrata Mondal and Lea F. Santos and S. Sinha},
journal= {arXiv preprint arXiv:2506.05475},
year = {2026}
}