On and Off-diagonal Sturmian operator: dynamic and spectral dimension

Abstract

We study two versions of quasicrystal model, both subcases of Jacobi matrices. For Off-diagonal model, we show an upper bound of dynamical exponent and the norm of the transfer matrix. We apply this result to the Off-diagonal Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large enough. In diagonal case, we improve previous lower bounds on the fractal box-counting dimension of the spectrum.

arXiv admin note: text overlap with arXiv:math-ph/0502044 and arXiv:0807.3024 by other authors

References in corpus (3)

• The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
• Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian
• Dynamical Bounds for Sturmian Schrödinger Operators

Cited by in corpus (2)

• Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian
• Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals