Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model
Spectral Theory
2018-04-24 v2
Abstract
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic quasiperiodic Jacobi operators in the positive Lyapunov exponent regime, we obtain a sharp arithmetic criterion of full spectral dimensionality. The applications include the extended Harper's model where we obtain arithmetic results on spectral dimensions and quantum dynamical exponents.
Keywords
Cite
@article{arxiv.1804.04322,
title = {Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model},
author = {Rui Han and Fan Yang and Shiwen Zhang},
journal= {arXiv preprint arXiv:1804.04322},
year = {2018}
}