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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Light-matter interactions

Background:

  • The Dicke model describes light-matter interactions in quantum systems.
  • Understanding transitions between ergodic and non-ergodic behavior is crucial for quantum chaos.
  • The interplay between different coupling terms influences system dynamics.

Purpose of the Study:

  • To investigate the ergodic-nonergodic transition in a generalized Dicke model.
  • To determine the relationship between this transition and the model's integrability.
  • To explore the connection between the transition and quantum phase transitions.

Main Methods:

  • Analysis of level statistics.
  • Calculation of the average ratio of consecutive level spacings.
  • Measurement of the quantum butterfly effect using out-of-time correlations.

Main Results:

  • The ergodic-nonergodic transition is linked to the model's proximity to an integrable limit when one coupling is zero.
  • This suggests a potential quantum analogue of the Kolmogorov-Arnold-Moser theorem.
  • No direct relationship was found between the ergodic-nonergodic transition and precursors of the normal-superradiant quantum phase transition.

Conclusions:

  • The generalized Dicke model exhibits an ergodic-nonergodic transition driven by integrability.
  • The findings offer insights into quantum chaos and its relation to integrability.
  • The study clarifies the distinction between ergodic transitions and quantum phase transition precursors.