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Emiliano M Fortes1, Ignacio García-Mata2, Rodolfo A Jalabert3

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Out-of-time-ordered correlators (OTOCs) reveal quantum chaos by examining long-time behavior. This study shows OTOCs accurately detect transitions between integrability and chaos in quantum systems.

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Area of Science:

  • Quantum mechanics
  • Quantum chaos
  • Statistical physics

Background:

  • Out-of-time-ordered correlators (OTOCs) are proposed probes for quantum chaos.
  • Their short-time exponential growth, previously linked to chaos, is not universally observed.
  • Investigating alternative manifestations of quantum chaos is necessary.

Purpose of the Study:

  • To explore quantum chaos manifestations beyond short-time OTOC growth.
  • To study the long-time behavior of OTOCs in diverse quantum systems.
  • To detect and quantify the transition from quantum integrability to chaos.

Main Methods:

  • Analysis of OTOCs' long-time dynamics.
  • Study of quantum maps (simplest chaotic one-body systems).
  • Investigation of spin chains (many-body systems without classical limits).
  • Benchmarking OTOC indicators against spectral and eigenstate properties.

Main Results:

  • Long-time OTOC behavior effectively detects and gauges the integrability-to-chaos transition.
  • OTOC indicators show high accuracy in systems with classical analogs.
  • Subtle features of the transition are discernible using OTOCs.

Conclusions:

  • The long-time regime of OTOCs provides a robust tool for identifying quantum chaos.
  • OTOCs offer a reliable method for characterizing the transition between integrability and chaos.
  • This approach is applicable to both simple and complex quantum systems.