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

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

2011-04-21

arxiv.org/abs/1104.4299v3

Physics

Mathematical Physics

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

Scientific paper

10.1142/S0129055X12500110

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.

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