07-110 David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian (67K, LaTeX) 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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