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

Qinghui Liu, Yiran Lv

math.DSarXiv:2609.12782

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: dimH sigma(Htm,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 mathbbR: dimH sigma(Htm,lambda)=1.

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