David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
(67K, LaTeX)
ABSTRACT. We study the spectrum of the Fibonacci Hamiltonian and prove upper
and lower bounds for its fractal dimension in the large coupling
regime. These bounds show that as $\lambda \to \infty$, $\dim
(\sigma(H_\lambda)) \cdot \log \lambda$ converges to an explicit
constant ($\approx 0.88137$). We also discuss consequences of these
results for the rate of propagation of a wavepacket that evolves
according to Schr\"odinger dynamics generated by the Fibonacci
Hamiltonian.