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arXiv · 0705.0338

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

David Damanik·Mark Embree·Anton Gorodetski·Serguei Tcheremchantsev
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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 $λ\to \infty$, $\dim (σ(H_λ)) \cdot \log λ$ 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 Schrödinger dynamics generated by the Fibonacci Hamiltonian.

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David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev. 2007-05-02. The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian. https://doi.org/10.1007/s00220-008-0451-3

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