Zero Hausdorff dimension spectrum for the almost Mathieu operator

DOI10.1007/S00220-016-2620-0zbMath1369.47039arXiv1510.07651OpenAlexW3100012159MaRDI QIDQ728478

Yoram Last, Mira Shamis

Publication date: 20 December 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07651

zbMATH Keywords

one-dimensional Schrödinger operators

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (11)

On the spectrum of critical almost Mathieu operators in the rational case ⋮ Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators ⋮ Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator ⋮ Magnetic square lattice with vertex coupling of a preferred orientation ⋮ Dynamics and spectral theory of quasi-periodic Schrödinger-type operators ⋮ Some remarks on the dynamics of the almost Mathieu equation at critical coupling* ⋮ Almost Mathieu operators with completely resonant phases ⋮ Central spectral gaps of the almost Mathieu operator ⋮ Zero measure spectrum for multi-frequency Schrödinger operators ⋮ Cantor spectra of magnetic chain graphs ⋮ Honeycomb structures in magnetic fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the measure of the spectrum for the almost Mathieu operator
• Gauss polynomials and the rotation algebra
• The coexistence problem for the discrete Mathieu operator
• On the measure of gaps and spectra for discrete 1D Schrödinger operators
• Positive Lyapunov exponents for a class of ergodic Schrödinger operators
• Zero measure spectrum for the almost Mathieu operator
• The Ten Martini problem
• Analyse semi-classique pour l'équation de Harper (avec application à l'équation de Schrödinger avec champ magnétique)
• Critical Binder cumulant in two-dimensional anisotropic Ising models
• A sum rule for the dispersion relations of the rational Harper equation
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)

This page was built for publication: Zero Hausdorff dimension spectrum for the almost Mathieu operator