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Solvable Models of Many-Body Chaos from Dual-Koopman Circuits.

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This study explores classical systems mirroring quantum chaos models. Researchers found these classical systems exhibit correlations vanishing on the light cone, governed by contractive maps, and can exhibit mixing behavior.

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Area of Science:

  • Statistical Mechanics
  • Quantum Chaos
  • Dynamical Systems

Background:

  • Dual-unitary circuits are key models for studying many-body quantum chaos.
  • Exact solutions for correlation functions and state time evolution are crucial in quantum chaos research.

Purpose of the Study:

  • To investigate classical counterparts of dual-unitary circuits using dual-canonical transformations and dual-Koopman operators.
  • To analyze the correlation properties and mixing behavior of these classical systems.

Main Methods:

  • Definition of dual-canonical transformations and dual-Koopman operators for classical many-body systems.
  • Analytical study of a coupled standard map as a detailed example.
  • Investigation of systems with "perfect" Koopman operators, including a cat-map lattice.

Main Results:

  • Classical systems exhibit correlations vanishing everywhere except on the light cone, where they decay via a contractive map.
  • The coupled standard map demonstrates mixing behavior in the thermodynamic limit, away from the integrable case.
  • A cat-map lattice is identified as a potential Bernoulli system, belonging to the highest level of the ergodic hierarchy.

Conclusions:

  • Dual-canonical transformations provide a framework for classical models of quantum chaos with predictable correlation decay.
  • These classical systems can exhibit complex dynamics, including mixing and properties associated with the ergodic hierarchy.
  • The study establishes a connection between quantum chaos models and classical dynamical systems with rich ergodic properties.