Transient and steady-state chaos in dissipative quantum systems

• URL: http://arxiv.org/abs/2506.05475v1
• Date: Thu, 05 Jun 2025 18:00:13 GMT
• Title: Transient and steady-state chaos in dissipative quantum systems
• Authors: Debabrata Mondal, Lea F. Santos, S. Sinha,
• Abstract summary: Dissipative quantum chaos plays a central role in the characterization and control of information scrambling, non-unitary evolution, and thermalization.<n>We introduce a random matrix toy model and show that Ginibre spectral statistics signals short-time chaos rather than steady-state chaos.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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