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Spectral statistics and localization properties of a C3-symmetric billiard

Matic Orel and Marko Robnik

  • Center for Applied Mathematics and Theoretical Physics (CAMTP), University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia, European Union

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Phys. Rev. E 114, 014220 – Published 21 July, 2026

DOI: https://doi.org/10.1103/s9jj-p8sy

Abstract

We revisit the spectral statistics of the C3-symmetric billiard introduced by F. Leyvraz et al. [J. Phys. A: Math. Gen. 29, L575 (1996)], which exhibits both Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE) statistics depending on the symmetry block. Using high-precision Beyn's contour-integral method for the nonlinear Fredholm eigenvalue problem with built-in separation of irreducible subspaces, we compute 2.8×105 eigenvalues in each symmetry subspace, enabling statistically meaningful comparisons with random matrix theory. The improved spectra reveal clear GOE-GUE correspondence and resolve previously observed deviations in long-range spectral correlations. Furthermore, we analyze phase-space eigenstate localization through the distribution of entropy localization measures, which, for chaotic states follow a β distribution whose standard deviation decays as a power law with energy, consistent with the onset of quantum ergodicity as described by Schnirelman's theorem.

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Phys. Rev. E 114, 014220– Published 21 July, 2026
  • Received 3 March 2026
  • Accepted 24 June 2026
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