Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator

Abstract

We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is positive.

arXiv comment3 figures

References in corpus (3)

• Hofstadter butterfly as Quantum phase diagram
• Central spectral gaps of the almost Mathieu operator
• Zero Hausdorff dimension spectrum for the almost Mathieu operator

Cited by in corpus (1)

• Magnetic square lattice with vertex coupling of a preferred orientation