Singular continuous spectrum on a cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian

It is rigorously proven that the spectrum of the tight-binding Fibonacci Hamiltonian,H _mn= _{m, n+1}+ _{m, n–1}+ _{m, n} (n+1)]–n]) where =(5–1)/2 and ·] means integer part, is a Cantor set of zero Lebesgue measure for all real nonzero, 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.On leave from the Central Research Institute for Physics, Budapest, Hungary.