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Classical chaos in atom-field systems.

J Chávez-Carlos1, M A Bastarrachea-Magnani1, S Lerma-Hernández2

  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Cd. Mx., Mexico, C.P. 04510.

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Summary
This summary is machine-generated.

Chaos and excited-state quantum phase transitions (ESQPTs) in atom-field systems arise from different mechanisms. Numerical studies of the Dicke model reveal distinct pathways for chaos onset and ESQPTs, challenging prior assumptions.

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Area of Science:

  • Quantum optics
  • Complex systems
  • Statistical mechanics

Background:

  • Quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs) are critical phenomena in quantum systems.
  • The relationship between chaos and ESQPTs in atom-field systems has been a subject of theoretical speculation.
  • Understanding these relationships is crucial for characterizing the dynamics of quantum systems.

Purpose of the Study:

  • To analyze the connection between the onset of chaos and critical phenomena (QPTs, ESQPTs) in atom-field systems.
  • To investigate whether ESQPTs are directly linked to the emergence of hard chaos, particularly in resonant and off-resonant regimes.
  • To differentiate the underlying mechanisms driving chaos and ESQPTs.

Main Methods:

  • Numerical simulations of the semiclassical Hamiltonian of the Dicke model.
  • Calculation of the largest Lyapunov exponent to quantify chaos.
  • Evaluation of the percentage of phase space exhibiting chaotic trajectories as a function of energy and coupling.
  • Mapping of ergodic properties in the coupling-energy space.

Main Results:

  • Chaos and ESQPTs in atom-field systems are driven by distinct physical mechanisms.
  • The onset of hard chaos is not solely associated with ESQPTs, especially in off-resonant cases.
  • Numerical analysis reveals specific regions in the coupling-energy space exhibiting ergodic properties.

Conclusions:

  • The study provides clear evidence that chaos and ESQPTs are independent phenomena in the analyzed atom-field systems.
  • The findings challenge the hypothesis linking hard chaos directly to ESQPTs, highlighting the importance of considering resonant and off-resonant conditions.
  • The detailed phase space analysis offers a comprehensive understanding of chaotic dynamics within the Dicke model.