1104.4299 (Laurent Marin)

On and Off-diagonal Sturmian operator: dynamic and spectral dimension    [PDF]

Laurent Marin

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.

View original: http://arxiv.org/abs/1104.4299