Abstract
It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,H mn=δ m, n+1+δ m, n−1+δ m, n μ[(n+1)α]−[nα]) where α=(√5−1)/2 and [·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzeroμ, and the spectral measures are purely singular continuous. This follows from a recent result by Kotani, coupled with the vanishing of the Lyapunov exponent in the spectrum.
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On leave from the Central Research Institute for Physics, Budapest, Hungary.
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Sütő, A. Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian. J Stat Phys 56, 525–531 (1989). https://doi.org/10.1007/BF01044450
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DOI: https://doi.org/10.1007/BF01044450