Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

1994/06/27 by Johannes Kellendonk, Kellendonk, Johannes
Materials Science · Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Analysis and Transform Methods #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #cond-mat #hep-th

paper · pdf · doi:10.48550/arxiv.cond-mat/9406107

13 pages, 1 figure, Latex, KCL-TH-94-10

arxiv created 1994/06/27 · openalex publication_date 1994/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed product with \Z^d. Penrose tilings belong to this class. This enlarges the class of tilings of which can be shown that a set of possible gap labels is completely determined by an invariant measure on the hull.

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