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Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems.

Jorge Chávez-Carlos1, B López-Del-Carpio1, Miguel A Bastarrachea-Magnani2

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The out-of-time-ordered correlator (OTOC) growth rate, a quantum chaos signature, matches the classical Lyapunov exponent in the interacting Dicke model. This validates quantum-classical chaos correspondence in complex systems.

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Area of Science:

  • Quantum chaos
  • Quantum information theory
  • Condensed matter physics

Background:

  • The exponential growth of the out-of-time-ordered correlator (OTOC) is a proposed quantum signature of classical chaos.
  • This quantum-classical correspondence has been confirmed for non-interacting systems like the kicked rotor and stadium billiard.
  • Validation in realistic, interacting quantum systems remains an open challenge.

Purpose of the Study:

  • To investigate the quantum-classical correspondence of chaos in an interacting quantum system.
  • To study the behavior of the OTOC in the chaotic regime of the Dicke model.
  • To determine if the OTOC growth rate aligns with the classical Lyapunov exponent in this model.

Main Methods:

  • Numerical analysis of the out-of-time-ordered correlator (OTOC).
  • Study of the Dicke model, a system with interacting two-level atoms and a quantized radiation field.
  • Comparison of OTOC growth rates with classical Lyapunov exponents in the chaotic regime.

Main Results:

  • The OTOC exhibits exponential growth in the chaotic regime of the Dicke model.
  • The growth rate of the OTOC closely follows the classical Lyapunov exponent.
  • This provides evidence for quantum-classical correspondence in a realistic, interacting system.

Conclusions:

  • The study validates the use of OTOC as a quantum signature of chaos in interacting systems.
  • The findings support the quantum-classical correspondence between OTOC growth and Lyapunov exponents.
  • The Dicke model serves as a crucial testbed for understanding quantum chaos in complex many-body systems.