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Data for The GOE ensemble for quasiperiodic tilings without unfolding: r-value statistics
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Grimm, Uwe and Roemer, Rudolf A. (2021) Data for The GOE ensemble for quasiperiodic tilings without unfolding: r-value statistics. [Dataset]
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Official URL: http://wrap.warwick.ac.uk/155668/
Abstract
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.
Item Type: | Dataset | ||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||
Type of Data: | numerical data in ASCII text file format | ||||||||
Library of Congress Subject Headings (LCSH): | Gaussian processes, Quasicrystals, Random matrices, Energy levels (Quantum mechanics) | ||||||||
Publisher: | University of Warwick, Department of Physics | ||||||||
Official Date: | 19 July 2021 | ||||||||
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Status: | Not Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Copyright Holders: | University of Warwick | ||||||||
Description: | The dataset contains |
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Date of first compliant deposit: | 19 July 2021 | ||||||||
Date of first compliant Open Access: | 19 January 2022 | ||||||||
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