Scaling of diffraction intensities near the origin: some rigorous results. (23rd May 2019)

• Record Type: Journal Article
• Authors: Baake, Michael; Grimm, Uwe
• Is Part Of: Journal of statistical mechanics. (2019:May)
• Publication Date: 2019-05-23
• Subjects: 3 -- 1 -- 9 -- 12; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab02f2
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation behaviour known under the term hyperuniformity. Here, we consider one-dimensional systems with pure point, singular continuous and absolutely continuous diffraction spectra, which include perfectly ordered cut and project and inflation point sets as well as systems with stochastic disorder.