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PreprintCC BY 4.0arXiv (Cornell University)

The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian

  • Qinghui Liu1
  • Yan-Hui Qu2
  1. 1Department of Computer Science, Beijing Institute of Technology, Beijing, 100081, Peoples’s Republic of China
  2. 2Department of Mathematics, Tsinghua University, Beijing, 100084, Peoples’s Republic of China
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Abstract

In 2015, Liu, Qu (Commun. Math. Phys., Vol. 338) show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian admits a positive lower bound independent of the coupling constant lambda: dim_H sigma(H_{tm,lambda}) ge (log 2) / (140log 2.1). In this paper, we prove that the spectrum of the Thue--Morse Hamiltonian has full Hausdorff dimension for any lambda in mathbb{R}: dim_H sigma(H_{tm,lambda})=1.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026hausdorff,
  title = {{The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian}},
  author = {Qinghui Liu and Yan-Hui Qu},
  howpublished = {arXiv (Cornell University)},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12782},
  eprint = {2609.12782},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12782},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian
AU  - Qinghui Liu
AU  - Yan-Hui Qu
PY  - 2026
DA  - 2026/09/11
PB  - arXiv (Cornell University)
DO  - 10.48550/arxiv.2609.12782
UR  - https://arxiv.org/abs/2609.12782
AB  - In 2015, Liu, Qu (Commun. Math. Phys., Vol. 338) show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian admits a positive lower bound independent of the coupling constant lambda: dim_H sigma(H_{tm,lambda}) ge (log 2) / (140log 2.1). In this paper, we prove that the spectrum of the Thue--Morse Hamiltonian has full Hausdorff dimension for any lambda in mathbb{R}: dim_H sigma(H_{tm,lambda})=1.
SN  - 2331-8422
ER  -