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Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

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Abstract

We consider discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive substitutions. Using the three-block version of Gordon's criterion, we establish purely singular continuous spectrum with probability one provided that the potentials have index greater than three. It is also shown that one cannot use this criterion to prove uniform results.

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Authors and Affiliations

  1. Department of Mathematics 253–37, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    David Damanik

  2. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054, Frankfurt, Germany

    David Damanik

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  1. David Damanik
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Damanik, D. Singular Continuous Spectrum for a Class of Substitution Hamiltonians II. Letters in Mathematical Physics 54, 25–31 (2000). https://doi.org/10.1023/A:1007697301341

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