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Transient and Steady-State Chaos in Dissipative Quantum Systems
Debabrata Mondal1, Lea F Santos2, S Sinha1
1Indian Institute of Science Education and Research-Kolkata, Mohanpur, Nadia-741246, India.
Physical Review Letters
|February 16, 2026
Summary
Dissipative quantum chaos is redefined using von Neumann entropy (VNE) and out-of-time-order correlators (OTOCs). These methods reveal distinct transient and steady-state chaos regimes, correcting previous spectral statistics assumptions.
Area of Science:
- Quantum physics
- Chaos theory
- Statistical mechanics
Background:
- Dissipative quantum chaos lacks a precise definition, hindering understanding of information scrambling, nonunitary evolution, and thermalization.
- The Grobe-Haake-Sommers conjecture, linking spectral statistics to classical chaos, has been shown to fail.
- Existing methods struggle to capture the full dynamics of quantum chaos in open systems.
Purpose of the Study:
- To restore the quantum-classical correspondence in dissipative quantum chaos.
- To introduce reliable diagnostics for identifying different regimes of quantum chaos.
- To clarify the role of spectral statistics in characterizing chaotic dynamics.
Main Methods:
- Utilizing von Neumann entropy (VNE) dynamics to track quantum chaos.
- Employing out-of-time-order correlators (OTOCs) as chaos indicators.
- Analyzing the open anisotropic Dicke model and a random matrix toy model.
Main Results:
- Two distinct regimes of dissipative quantum chaos were identified: transient and steady-state.
- Transient chaos shows rapid early-time VNE/OTOC growth with low saturation.
- Steady-state chaos is characterized by high long-time VNE/OTOC values.
- Ginibre spectral statistics were found to indicate short-time chaos, not steady-state chaos.
Conclusions:
- VNE dynamics and OTOCs provide reliable diagnostics for dissipative quantum chaos.
- The study establishes a robust quantum-classical correspondence beyond spectral properties.
- A clear distinction between short-time and long-time chaotic behaviors is demonstrated.
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