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The quantum three-rotor problem reveals transitions between order and chaos in coupled Josephson junctions. Energy level distributions show quantum signatures of chaos, shifting from Poisson to Wigner-Dyson statistics at strong coupling.

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Area of Science:

  • Quantum mechanics
  • Chaos theory
  • Condensed matter physics

Background:

  • The quantum three-rotor problem models coupled Josephson junctions, exhibiting order-chaos-order behavior classically.
  • Quantum systems show semiclassical behavior at strong coupling, necessitating study of stationary states.

Purpose of the Study:

  • Investigate quantum hallmarks of chaos in the three-rotor system.
  • Analyze energy level distributions and spectral statistics across different coupling regimes.

Main Methods:

  • Numerical diagonalization and perturbative/harmonic approximations to study energy spectra.
  • Exploiting S3×Z2 symmetry with invariant states for spectral analysis.
  • Partitioning spectra into energy windows (regular, mixed, chaotic) for detailed analysis.

Main Results:

  • Spacing distributions transition from Poisson to Wigner-Dyson at strong coupling, indicating quantum chaos.
  • Number variance shifts from linear to logarithmic, revealing chaos signatures.
  • Nonuniversal features like saturated/oscillating number variance and spectral form factor peaks observed.

Conclusions:

  • The quantum three-rotor system exhibits clear signatures of transitions between regularity and chaos.
  • Semiclassical estimates and symmetry analysis provide insights into spectral properties.
  • Deviations from Poisson statistics are explained by projected quantum harmonic and free-rotor spectra.