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Spectral Properties of Continuum Fibonacci Schr\"odinger Operators

Spectral Theory 2018-03-28 v1 Mathematical Physics Dynamical Systems math.MP

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.

Keywords

Cite

@article{arxiv.1702.04337,
  title  = {Spectral Properties of Continuum Fibonacci Schr\"odinger Operators},
  author = {Jake Fillman and May Mei},
  journal= {arXiv preprint arXiv:1702.04337},
  year   = {2018}
}