Aperiodic order and pure point diffraction

Abstract

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems.

14 pages

References in corpus (13)

• Pure Point Dynamical and Diffraction Spectra
• Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
• Characterizations of model sets by dynamical systems
• Which distributions of matter diffract? - Some answers
• Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems
• Pure point diffraction and cut and project schemes for measures: The smooth case
• Deformation of Delone dynamical systems and pure point diffraction
• Substitution Delone Sets with Pure Point Spectrum are Inter Model Sets
• Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies
• A Characterization of Model Multi-colour Sets
• Pinwheel patterns and powder diffraction
• Diffraction spectrum of lattice gas models above T_c
• Continuity of eigenfunctions of uniquely ergodic dynamical systems and intensity of Bragg peaks

Cited by in corpus (12)

• Symmetry Breaking and Order in the Age of Quasicrystals
• Pure Point spectrum for measure dynamical systems on locally compact Abelian groups
• Kinematic Diffraction from a Mathematical Viewpoint
• On the Fourier Analysis of Measures with Meyer Set Support
• Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra
• The Pisot Conjecture for $\beta$-substitutions
• Some comments on pinwheel tilings and their diffraction
• A note on measures vanishing at infinity
• On the Fourier Transformability of Strongly Almost Periodic Measures
• Model sets with precompact Borel windows
• Nanotechnology and Quasicrystals: From self assembly to photonic applications
• Measures on the Spectra of Algebraic Integers