Abstract
The spectrum σ(H) of the tight binding Fibonacci Hamiltonian (H mn=δ m,n+1+δ m+1,n +δ m,n μv(n),v(n)=\(\chi _{[ - \omega ^3 ,\omega ^2 [} \)((n−1)ω), 1/ω is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any μ, and σ(H) is a Cantor set for ∣μ∣≧4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for ∣μ∣≧16.
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Communicated by B. Simon
On leave from the Central Research Institute for Physics, Budapest, Hungary
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Sütő, A. The spectrum of a quasiperiodic Schrödinger operator. Commun.Math. Phys. 111, 409–415 (1987). https://doi.org/10.1007/BF01238906
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DOI: https://doi.org/10.1007/BF01238906