Smooth perturbation theory and generic Cantor spectrum for multi-dimensional monotone quasiperiodic operators

arXiv:2610.00733 · math.SP, math-ph, math.MP, quant-ph · Submitted 2026-09-30 · Read on arXiv

math.SP, math-ph, math.MP, quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Spectral Gap — 18× in this paper · explained in 5 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Dry Ten Martini Problem in the non-critical case
• The Dry Ten Martini Problem for Sturmian Hamiltonians
• Absence of flat bands for discrete periodic graph operators with generic potentials
• Kotani theory, Puig's argument, and stability of The Ten Martini Problem
• Sharp arithmetic localization for quasiperiodic operators with monotone potentials
• Monotonicity, global symplectification and the stability of Dry Ten Martini Problem