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arXiv · 1804.04322

Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model

Rui Han·Fan Yang·Shiwen Zhang
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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.

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Rui Han, Fan Yang, Shiwen Zhang. 2018-04-12. Spectral Dimension for $\beta$-almost periodic singular Jacobi operators and the extended Harper's model. https://arxiv.org/abs/1804.04322

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