Cantor spectrum for multidimensional quasi-periodic Schrödinger operators
Abstract
Abstract In this paper, we prove that for a dense set of irrational frequencies with positive Hausdorff dimension, the Hausdorff (and upper box) dimension of the spectrum of the critical almost Mathieu operator is positive, yet can be made arbitrarily small. As a consequence, we investigate the spectrum of a class of multidimensional quasi-periodic Schrödinger operators that exhibit a Cantor spectrum, which answers a question posed by Damanik, Fillman, and Gorodetski [24].
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quasicrystal Structures and Properties
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Forum of Mathematics Sigma
- Volume
- 14
- Publication date
- 1 January 2026
- Language
- EN