The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

Details The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

2007-05-02

arxiv.org/abs/0705.0338v1

Physics

Mathematical Physics

23 pages

Scientific paper

10.1007/s00220-008-0451-3

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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