1995/10/12 by Anton Bovier, Bovier, Anton, J. -M. Ghez +2
Materials Science · Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Mathematical functions and polynomials #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9510061
arxiv created 1995/10/12 · openalex publication_date 1995/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Schrödinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically verifiable sufficient condition for their spectrum to be singular continuous and supported on a Cantor set of zero Lebesgue measure. Applications to specific examples are discussed.