On and Off-diagonal Sturmian operator: dynamic and spectral dimension
Mathematical Physics
2012-04-24 v3 math.MP
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.
Cite
@article{arxiv.1104.4299,
title = {On and Off-diagonal Sturmian operator: dynamic and spectral dimension},
author = {Laurent Marin},
journal= {arXiv preprint arXiv:1104.4299},
year = {2012}
}
Comments
arXiv admin note: text overlap with arXiv:math-ph/0502044 and arXiv:0807.3024 by other authors