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Spacing ratios in mixed-type systems.

Hua Yan1

  • 1CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia.

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Summary
This summary is machine-generated.

This study analytically derives the distribution of spacing ratios for mixed quantum systems. The findings help distinguish between integrable and chaotic quantum spectra using random matrix theory.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • The consecutive level-spacing ratio is a key metric for differentiating integrable from chaotic quantum spectra.
  • This method circumvents the need for numerical spectral unfolding, a common challenge in spectral analysis.

Purpose of the Study:

  • To analytically derive the distribution of spacing ratios for random matrices composed of independent integrable and chaotic blocks.
  • To extend the Rosenzweig-Porter approach for analyzing level spacings in mixed-type quantum systems.

Main Methods:

  • Analytical derivation using random matrix theory.
  • Extension of the Rosenzweig-Porter approach.
  • Numerical confirmation using paradigmatic models like the quantum kicked rotor and Hénon-Heiles system.

Main Results:

  • An analytical formula for the distribution of spacing ratios in systems with independent integrable and chaotic blocks was derived.
  • The derived distribution was numerically validated, confirming its accuracy.

Conclusions:

  • The analytical approach provides a robust method for characterizing quantum spectral properties.
  • This work offers a valuable tool for analyzing complex quantum systems and distinguishing spectral behaviors.