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.