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

Han Rui; Yang Fan; Zhang Shiwen

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

机译：β-几乎定期奇异雅各比运营商和延长哈珀模型的光谱维度

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摘要

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.

机译：研究了奇异雅可比算子的分形维数性质。我们证明了具有强重复性和受控奇异性的一般算子的定量谱/量子动力学下界。对于正Lyapunov指数区域的解析拟周期Jacobi算子，我们得到了一个全谱维数的精确算术判据。这些应用包括扩展的哈珀模型，在该模型中，我们获得了关于光谱维度和量子动力学指数的算术结果。

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《Journal d'analyse mathematique》 |2020年第2期|共62页
作者
Han Rui; Yang Fan; Zhang Shiwen;
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Georgia Inst Technol Sch Math Atlanta GA 30332 USA;

Georgia Inst Technol Sch Math Atlanta GA 30332 USA;

Michigan State Univ Dept Math E Lansing MI 48824 USA;

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正文语种 eng
中图分类数学分析;
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Spectral dimension for beta-almost periodic singular Jacobi operators and the extended Harper's model

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