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.

13 pages

References in corpus (3)

• The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
• Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian
• Eigenvalue Spacings and Dynamical Upper Bounds for Discrete One-Dimensional Schroedinger Operators

Cited by in corpus (1)

• Transport Exponents of Sturmian Hamiltonians