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

TL;DR

This paper establishes a universal positive lower bound for the Hausdorff dimension of the spectrum associated with the Thue-Morse Hamiltonian across all coupling strengths, advancing understanding of its spectral properties.

Contribution

It proves that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a uniform positive lower bound for all coupling values, a novel result in spectral theory.

Findings

Hausdorff dimension has a positive lower bound

Bound is uniform across all coupling strengths

Advances understanding of spectral properties of Thue-Morse Hamiltonian

Abstract

We show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a common positive lower bound for all coupling.