Scaling of diffraction intensities near the origin: some rigorous results

Baake, Michael and Grimm, Uwe (2019). Scaling of diffraction intensities near the origin: some rigorous results. Journal of Statistical Mechanics: Theory and Experiment, May 2019, article no. 054003.

DOI: https://doi.org/10.1088/1742-5468/ab02f2

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.

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About

• Item ORO ID
• 61434
• Item Type
• Journal Item
• ISSN
• 1742-5468
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Lyapunov Exponents and Spectral Properties of Aperiodic Structures	EP/S010335/1	EPSRC (Engineering and Physical Sciences Research Council)

• Keywords
• renormalisation group; rigorous results in statistical mechanics; random/ordered microstructures; stochastic processes
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2019 IOP Publishing Ltd and SISSA Medialab srl
• Depositing User
• Uwe Grimm