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We study fractal dimension properties of singular Jacobi operators. We provequantitative lower spectral/quantum dynamical bounds for general operators withstrong repetition properties and controlled singularities. For analyticquasiperiodic Jacobi operators in the positive Lyapunov exponent regime, weobtain a sharp arithmetic criterion of full spectral dimensionality. Theapplications include the extended Harper's model where we obtain arithmeticresults on spectral dimensions and quantum dynamical exponents.

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