# The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

@article{Damanik2008TheFD, title={The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian}, author={David Damanik and Mark Embree and Anton Gorodetski and Serguei Tcheremchantsev}, journal={Communications in Mathematical Physics}, year={2008}, volume={280}, pages={499-516} }

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 $$\lambda \to \infty, {\rm dim} (\sigma(H_\lambda)) \cdot {\rm log} \lambda$$converges to an explicit constant, $${\rm log}(1+\sqrt{2})\approx 0.88137$$ . 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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