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Level Compressibility of Certain Random Unitary Matrices.

Eugene Bogomolny1

  • 1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.

Entropy (Basel, Switzerland)
|June 24, 2022
PubMed
Summary
This summary is machine-generated.

This study analytically calculates level compressibility for random unitary matrices. The research proves this value is consistently 1/2 for barrier billiards, regardless of barrier specifics.

Keywords:
barrier billiardslevel compressibility

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Area of Science:

  • Quantum Chaos
  • Mathematical Physics
  • Spectral Theory

Background:

  • Spectral form factor at the origin, or level compressibility, is key for random spectra analysis.
  • Understanding intermediate spectral statistics in random unitary matrices is crucial.

Purpose of the Study:

  • To perform analytical calculations of level compressibility for various random unitary matrices.
  • To investigate spectral statistics in models with intermediate properties.

Main Methods:

  • Utilizing G. Tanner's approach for chaotic systems.
  • Determining eigenvalues of a transition matrix derived from initial unitary matrices.

Main Results:

  • Analytical calculation of level compressibility for specific random unitary matrices.
  • Proof that level compressibility equals 1/2 for random unitary matrices from barrier billiards.

Conclusions:

  • The level compressibility of random unitary matrices from barrier billiards is 1/2.
  • This result is independent of barrier height and position.