07-110 David Damanik, Mark Embree, Anton Gorodetski, Serguei Tcheremchantsev
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian (67K, LaTeX) May 2, 07
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 $\lambda \to \infty$, $\dim (\sigma(H_\lambda)) \cdot \log \lambda$ 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.

Files: 07-110.src( 07-110.keywords , DEGT.TEX )