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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Qinghui Liu, Yan-Hui Qu
DOI: 10.48550/arxiv.2609.12782
Cited by: 10
References: 42

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.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Topological and Geometric Data Analysis Quantum chaos and dynamical systems

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 September 2026
Language
EN
Document type
Preprint