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Transient and Steady-State Chaos in Dissipative Quantum Systems.

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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.

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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.