Jitomirskaya S., Last Y.
Dimensional Hausdorff Properties of Singular Continuous Spectra
(27K, LaTeX)
ABSTRACT. We present an extension of the Gilbert-Pearson theory of subordinacy,
which relates dimensional Hausdorff spectral properties of one-dimensional
Schr\"odinger operators to the behavior of solutions of the corresponding
Schr\"odinger equation. We use this theory to analyze these properties for
several examples having singular-continuous spectrum, including sparse
barrier potentials, the almost Mathieu operator and the Fibonacci
Hamiltonian. (to appear in Phys. Rev. Lett.)