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Missing-level statistics in classically chaotic quantum systems with symplectic symmetry.

Jiongning Che1, Junjie Lu1,2, Xiaodong Zhang1

  • 1Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou University, Lanzhou, Gansu 730000, China.

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We present a new random-matrix theory (RMT) approach for analyzing incomplete quantum spectra. This method accurately predicts fluctuation properties in systems with symplectic symmetry and chaotic dynamics, even with missing data.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • Understanding quantum systems with chaotic dynamics is crucial.
  • Incomplete spectra pose challenges for traditional analysis.
  • Random-matrix theory (RMT) is a powerful tool for spectral analysis.

Purpose of the Study:

  • To extend RMT for analyzing incomplete quantum spectra with symplectic symmetry.
  • To validate theoretical predictions against numerical and experimental data.
  • To demonstrate the applicability of the extended RMT approach.

Main Methods:

  • Extending the RMT approach for incomplete spectra.
  • Numerical simulations using quantum graphs.
  • Experimental analysis of microwave networks.
  • Comparing fluctuation properties of incomplete spectra with RMT predictions.

Main Results:

  • Validated RMT predictions for incomplete spectra with symplectic symmetry.
  • Demonstrated the method's applicability to both numerical and experimental data.
  • Showcased that RMT can identify the fraction of missing levels and symmetry class.

Conclusions:

  • The extended RMT approach provides accurate predictions for incomplete quantum spectra.
  • This method is robust and applicable across different symmetry classes.
  • It enables reliable analysis of quantum systems even with partial spectral data.