2026-10-13T03:37:30Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33825400 2026-09-15T21:43:13Z portal_1197 item_type_3 month_year_09_2026

Data for The GOE ensemble for quasiperiodic tilings without unfolding: r-value statistics Uwe Grimm (24843685) Rudolf A. Roemer (22037333) Gaussian processes Quasicrystals Random matrices Energy levels (Quantum mechanics) Migrated from ePrints We study the level-spacing statistics for non-interacting Hamiltonians defined on the two-dimensional quasiperiodic Ammann--Beenker (AB) tiling. When applying the numerical procedure of "unfolding", these spectral properties in each irreducible sector are known to be well-described by the universal Gaussian orthogonal random matrix ensemble. However, the validity and numerical stability of the unfolding procedure has occasionally been questioned due to the fractal self-similarity in the density of states for such quasiperiodic systems. Here, using the so-called r-value statistics for random matrices, P(r), for which no unfolding is needed, we show that the Gaussian orthogonal ensemble again emerges as the most convincing level statistics for each irreducible sector. The results are extended to random-AB tilings where random flips of vertex connections lead to the irreducibility.<br><br>The dataset contains - data-QP.zip: zipped .dat eigenvalue data and .inp input files to generate for quasi-periodic (QP) 2D Ammann-Beenker tilings for differnent inflation levels, sectors and parities. For example, the directory QPr-ABFSH3-4--1 contains data and input files for inflation 3, sector 4 and paraity -1. - data-RAND.zip: zipped .dat eigenvalue data and .inp input files to generate for random (RAND) quasi-periodic 2D Ammann-Beenker tilings for differnent inflation levels and vertex flips. For example, the directory QPr-ABPN4-1-10 contains data and input files for inflation 4, diagonalized by taking into account the bipartness of the spectrum (1) and for 10 flips. Each .dat files in both .zip folders has in the 1st lines some information about the number of eigenvalues to follow. - SpacingDistribution5times5.nb is a Mathematica [(c) Wolfram Research] notebook to compute the 5 by 5 estimate for PGOE(r). 2021-07-19T00:00:00Z Dataset Dataset 10.82444/warw.33825400.v1 https://figshare.com/articles/dataset/Data_for_The_GOE_ensemble_for_quasiperiodic_tilings_without_unfolding_r-value_statistics/33825400 CC BY 4.0