标题： Fibonacci Hamiltonian 谱的分形维度 显示英文标题

标题： The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

摘要： 我们研究了 Fibonacci 哈密顿量的谱，并在大耦合强度下证明了其分形维数的上下界。 这些界表明当 $\lambda \to \infty$ 时，$\dim (\sigma(H_\lambda)) \cdot \log \lambda$ 收敛到一个明确的常数 ($\approx 0.88137$)。 我们还讨论了这些结果对由 Fibonacci 哈密顿量生成的薛定谔动力学中波包传播速率的影响。 显示英文摘要

摘要： 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.