Transient and steady-state chaos in dissipative quantum systems

TL;DR

This paper investigates dissipative quantum chaos using entanglement entropy and out-of-time-order correlators, revealing distinct transient and steady-state chaotic regimes in the open anisotropic Dicke model.

Contribution

It introduces a dynamical approach to characterize quantum chaos beyond spectral statistics, clarifying the roles of entanglement and OTOCs in different chaotic regimes.

Findings

Transient chaos shows rapid early entanglement and OTOC growth with low saturation.

Steady-state chaos exhibits high long-time entanglement and OTOC values.

Ginibre spectral statistics signal short-time chaos, not steady-state chaos.

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.