Schrödinger operators generated by substitutions

Anton Bovier; J. -M. Ghez

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arXiv · cond-mat/9510061

Schrödinger operators generated by substitutions

Anton Bovier·J. -M. Ghez

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Abstract

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.

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Anton Bovier, J. -M. Ghez. 1995-10-12. Schrödinger operators generated by substitutions. https://arxiv.org/abs/cond-mat/9510061

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