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Measure Zero Spectrum of a Class of Schrödinger Operators

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Abstract

We study the measure of the spectrum of a class of one-dimensional discrete Schrödinger operators H vω with potential v(ω) generated by any primitive substitutions. It is well known that the spectrum of H vω is singular continuous.(1) We will give a more exact result that the spectrum of H vω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.(2)

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Liu, QH., Tan, B., Wen, ZX. et al. Measure Zero Spectrum of a Class of Schrödinger Operators. Journal of Statistical Physics 106, 681–691 (2002). https://doi.org/10.1023/A:1013718624572

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