 07110 David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev
 The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
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May 2, 07

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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.
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