Spectral Properties of Continuum Fibonacci Schrödinger Operators

Abstract

We study continuum Schrödinger 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.

References in corpus (2)

• The Fibonacci Hamiltonian
• Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications

Cited by in corpus (1)

• Schrödinger Operators with Thin Spectra