Spectral analysis of tridiagonal Fibonacci Hamiltonians

Abstract

We consider a family of discrete Jacobi operators on the one-dimensional integer lattice, with the diagonal and the off-diagonal entries given by two sequences generated by the Fibonacci substitution on two letters. We show that the spectrum is a Cantor set of zero Lebesgue measure, and discuss its fractal structure and Hausdorff dimension. We also extend some known results on the diagonal and the off-diagonal Fibonacci Hamiltonians.

28 pages, 55 references, 4 figures

References in corpus (4)

• Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian
• Electronic Energy Spectra of Square and Cubic Fibonacci Quasicrystals
• Electronic energy spectra and wave functions on the square Fibonacci tiling
• On the spectrum of 1D quantum Ising quasicrystal

Cited by in corpus (10)

• The Fibonacci Hamiltonian
• Continuum Schrödinger Operators Associated With Aperiodic Subshifts
• Quantum and Spectral Properties of the Labyrinth Model
• Dynamical Green Functions and Discrete Schrödinger Operators with Potentials Generated by Primitive Invertible Substitution
• Properties of 1D classical and quantum Ising quasicrystals: rigorous results
• On the spectrum of 1D quantum Ising quasicrystal
• Purely singular continuous spectrum for CMV operators generated by subshifts
• Spectral Properties of Continuum Fibonacci Schrödinger Operators
• Newhouse phenomena in the Fibonacci trace map
• Finite section method for aperiodic Schrödinger operators