# The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian - Mathematical Physics

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Abstract: We study the spectrum of the Fibonacci Hamiltonian and prove upper and lowerbounds for its fractal dimension in the large coupling regime. These boundsshow that as $\lambda \to \infty$, $\dim (\sigma(H \lambda)) \cdot \log\lambda$ converges to an explicit constant ($\approx 0.88137$). We also discussconsequences of these results for the rate of propagation of a wavepacket thatevolves according to Schr\-odinger dynamics generated by the FibonacciHamiltonian.

Author: David Damanik (Rice), Mark Embree (Rice), Anton Gorodetski (Caltech), Serguei Tcheremchantsev (Universite d'Orleans)

Source: https://arxiv.org/