A short guide to pure point diffraction in cut-and-project sets*We dedicate this work to Tony Guttmann on the occasion of his 70th birthday. (14th March 2017)

• Record Type: Journal Article
• Authors: Richard, Christoph; Strungaru, Nicolae
• Is Part Of: Journal of physics. Volume 50:Number 15(2017)
• Publication Date: 2017-03-14
• Subjects: regular model set -- cut-and-project scheme -- Poisson summation formula -- diffraction; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa5d44
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.