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

TL;DR

This paper investigates the spectral and dynamical properties of off-diagonal and diagonal Sturmian operators, providing bounds on dynamical exponents and spectrum dimensions, with applications to Fibonacci Hamiltonians.

Contribution

It introduces new bounds on dynamical exponents and spectrum dimensions for Sturmian operators, advancing understanding of quasicrystal models.

Findings

Upper bounds on dynamical exponents for off-diagonal models

Sub-ballistic transport bounds for large coupling Fibonacci Hamiltonians

Improved lower bounds on spectral fractal dimensions

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.