Schrödinger operators generated by substitutions

Details Schrödinger operators generated by substitutions Schrödinger operators generated by substitutions

1995-10-12

arxiv.org/abs/cond-mat/9510061v1

Physics

Condensed Matter

Scientific paper

Schr\"odinger 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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