The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

الأصل · EN

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→ ∞, (σ(Hλ)) · λ converges to an explicit constant (≈ 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.