Almost ballistic transport for the weakly coupled Fibonacci Hamiltonian

Abstract

We prove estimates for the transport exponents associated with the weakly coupled Fibonacci Hamiltonian. It follows in particular that the upper transport exponent \(\tilde \alpha _u^ \pm \) approaches the value one as the coupling goes to zero. Moreover, for sufficiently small coupling, \(\tilde \alpha _u^ \pm \) strictly exceeds the fractal dimension of the spectrum.