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}
}