Spectral statistics and localization properties of a $C_3$-symmetric billiard

• URL: http://arxiv.org/abs/2603.03460v1
• Date: Tue, 03 Mar 2026 19:16:28 GMT
• Title: Spectral statistics and localization properties of a $C_3$-symmetric billiard
• Authors: Matic Orel, Marko Robnik,
• Abstract summary: We revisit the spectral statistics of the C$_3$--symmetric billiard introduced by Dembowski.<n>We compute 2.8x10$5$ eigenvalues in each symmetry subspace, enabling statistically meaningful comparisons with random matrix theory.<n>The improved spectra reveal clear GOE--GUE correspondence and resolve previously observed deviations in long--range spectral correlations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the spectral statistics of the C$_3$--symmetric billiard introduced by Dembowski [Phys. Rev. E, R4516 (2000)], which exhibits both GOE and 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 2.8x10$^5$ 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 Beta 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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