Pure Point Dynamical and Diffraction Spectra
By Jeong-Yup Lee, Robert V. Moody, Boris Solomyak. 2002
190 citations recorded by the source corpus.
Abstract. We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
Subfields: Geometry and Topology, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/92cd16aa839aea7fecf40c27b50aa72c51d89e3e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Gerhard Keller
- Christoph Richard
- Jörg M. Thuswaldner
- Shigeki Akiyama
- Robert V. Moody
- Michael Baake
- Val'erie Berth'e
- Anne Siegel
In Materials Chemistry
- Gerhard Keller
- Christoph Richard
- Michael Baake
- Jörg M. Thuswaldner
- Anne Siegel
- Shigeki Akiyama
- Marcy Barge
- Val'erie Berth'e
Citations in the corpus
- On the Pisot Substitution Conjecture (2015, background): “For example, if T is a primitive FLC substitution tiling in R n and Γ T = =1 Γ i × { i } is a substitution Delone multi-color set associated with T , then each Γ i has pure point diffraction spectrum if and only if (Ω T , R n ) has pure discrete spectrum ([17, 18, 48, 60, 80, 81, 82, 102]).”
- Quasicrystals : structure and physical properties (2003, unknown): “which are obtained by lattice substitution systems via Delone multisets15. They are the natural generalisation of one dimensional substitution rules with constant length, and it was recently possible [15, 16, 17] to find a complete generalisation of Dekking’s coincidence criterion (see [18]) to this ”
- Weighted Dirac combs with pure point diffraction (2002, background): “The second is to look at the dynamical system constructed from the hull of the quasicrystal under translation and to connect the diffraction with the corresponding dynamical spectrum [37, 36, 26].”
- Dynamics on the graph of the torus parametrization (2015, background): “This, in turn, implies that any regular model set has pure point diffraction spectrum [35, 6].”
- Topological Properties of Rauzy Fractals (2010, background): “The question whether such a material is a quasi-crystal has been studied in the 1990s: Lee, Moody and Solomyak proved that if the substitution is Pisot (its abelianized matrix has a unique expanding direction), then its diffraction spectrum is purely discrete if and only if the dynamical spectrum of”