Spectral Properties of Continuum Fibonacci Schr\"odinger Operators

Jake Fillman; May Mei

doi:10.1007/s00023-017-0624-8

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arXiv · 1702.04337

Spectral Properties of Continuum Fibonacci Schr\"odinger Operators

Jake Fillman·May Mei

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Abstract

We study continuum Schr\"odinger operators on the real line whose potentials are comprised of two compactly supported square-integrable functions concatenated according to an element of the Fibonacci substitution subshift over two letters. We show that the Hausdorff dimension of the spectrum tends to one in the small-coupling and high-energy regimes, regardless of the shape of the potential pieces.

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BibTeX RIS

Jake Fillman, May Mei. 2017-02-14. Spectral Properties of Continuum Fibonacci Schr\"odinger Operators. https://doi.org/10.1007/s00023-017-0624-8

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