SCD Patterns Have Singular Diffraction

Details SCD Patterns Have Singular Diffraction SCD Patterns Have Singular Diffraction

2004-11-15

arxiv.org/abs/math-ph/0411052v1

Physics

Mathematical Physics

11 pages, 2 figures; Accepted for Journal of Mathematical Physics

Scientific paper

10.1063/1.1842355

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part, that they have a uniformly discrete pure point part on the z-axis, and that they are otherwise supported on a set of concentric cylinder surfaces around this axis. For SCD tilings with additional properties, more detailed results are given.

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