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

2018/04/12 by Rui Han, Fan Yang, Han, Rui +3
Materials Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Magnetism in coordination complexes #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1804.04322

openalex publication_date 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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