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

RESUMO

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.