The Hausdorff dimension of the spectrum of a class of generalized Thue-Morse Hamiltonians

DOI10.1007/s10473-023-0504-xzbMath1524.28007MaRDI QIDQ6171219

Qing-Hui Liu, Zhiyi Tang

Publication date: 17 July 2023

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionone-dimensional Schrödinger operatorgeneralized Thue-Morse sequence

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Random linear operators (47B80) Hausdorff and packing measures (28A78)

Cites Work

• Uniform convergence of Schrödinger cocycles over bounded Toeplitz subshift
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• Singular continuous spectrum on a Cantor set of zero Lebesgue measure for the Fibonacci Hamiltonian
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• Theory of nonlinear lattices.
• Spectral properties of one-dimensional Schrödinger operators with potentials generated by substitutions
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• Measure zero spectrum of a class of Schrödinger operators
• Spectral properties of one dimensional quasi-crystals
• Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals
• The spectrum of period-doubling Hamiltonian
• On the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian
• Uniform convergence of Schrödinger cocycles over simple Toeplitz subshift
• Dimension of the spectrum of one-dimensional discrete Schrödinger operators with Sturmian potentials
• A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem

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