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This study reveals a universal connection between quantum chaos measures and finite-time classical dynamics. Findings suggest this finite-time quantum-classical correspondence applies broadly, enhancing understanding of quantum systems.

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Area of Science:

  • Quantum Chaos
  • Quantum Dynamics
  • Classical Mechanics

Background:

  • Quantum-classical correspondence is crucial for quantum chaos.
  • Understanding quantum chaos via finite-time classical dynamics is limited.
  • Mixed-type systems are key to exploring this correspondence.

Purpose of the Study:

  • To analyze the relationship between quantum chaotic measures and finite-time classical trajectory chaos.
  • To determine if this relationship is universal across different systems.
  • To enhance the understanding of quantum-classical correspondence in chaotic systems.

Main Methods:

  • Detailed analysis of quantum chaotic measures.
  • Examination of chaoticity in finite-time classical trajectories.
  • Systematic study of time-dependent and many-body systems.

Main Results:

  • A strong correspondence was found between quantum chaos and finite-time classical dynamics.
  • This dependence is described by a system-independent function.
  • The findings were validated in mixed-type, time-dependent, and many-body systems.

Conclusions:

  • Finite-time quantum-classical correspondence demonstrates universal validity.
  • This work provides a new approach to study the ergodic hierarchy in quantum systems.
  • The findings deepen the comprehension of quantum-classical correspondence.