Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum

Abstract

We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.

8 pages

References in corpus (6)

• Bethe-Sommerfeld Conjecture
• Periodic quantum graphs from the Bethe-Sommerfeld perspective
• Discrete Bethe-Sommerfeld Conjecture
• Periodic and limit-periodic discrete Schrödinger operators
• Discrete Bethe--Sommerfeld Conjecture for Triangular, Square, and Hexagonal Lattices
• Spectra of Discrete Two-Dimensional Periodic Schrödinger Operators with Small Potentials

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• Schrödinger Operators with Thin Spectra
• On the spectra of separable 2D almost Mathieu operators
• Bloch wave approach to almost periodic homogenization and approximations of effective coefficients
• Stahl--Totik regularity for continuum Schrödinger operators
• Stahl-Totik Regularity for Dirac Operators