Title
Spectral dimension for β-almost periodic singular Jacobi operators and the extended Harper’s model
Document Type
Article
Publication Date
11-1-2020
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.
Publication Source (Journal or Book title)
Journal d'Analyse Mathematique
First Page
605
Last Page
666
Recommended Citation
Han, R., Yang, F., & Zhang, S. (2020). Spectral dimension for β-almost periodic singular Jacobi operators and the extended Harper’s model. Journal d'Analyse Mathematique, 142 (2), 605-666. https://doi.org/10.1007/s11854-020-0145-0