Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
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- Sütő, A. J Stat Phys (1989) 56: 525. doi:10.1007/BF01044450
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It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,Hmn=δm, n+1+δm, n−1+δm, nμ[(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.