Stability of the gapless pure point spectrum of self-adjoint operators

DOI10.1063/5.0187017arXiv2211.05670OpenAlexW4392458771MaRDI QIDQ6123732

Paolo Facchi, Marilena Ligabò

Publication date: 8 April 2024

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

Full work available at URL: https://arxiv.org/abs/2211.05670

Mathematics Subject Classification ID

Partial differential equations (35-XX) Quantum theory (81-XX)

Cites Work

• Localization for a class of one dimensional quasi-periodic Schrödinger operators
• Examples of discrete Schrödinger operators with pure point spectrum
• A metal-insulator transition for the almost Mathieu model
• Localization in \(\nu\)-dimensional incommensurate structures
• Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
• The one-dimensional Schrödinger equation with a quasiperiodic potential
• Duality and singular continuous spectrum in the almost Mathieu equation
• Absolutely continuous spectrum for 1D quasiperiodic operators.
• All couplings localization for quasiperiodic operators with monotone potentials
• Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
• Metal-insulator transition for the almost Mathieu operator
• Convergence of perturbation series for unbounded monotone quasiperiodic operators
• Arithmetic Spectral Transitions for the Maryland Model
• Localization for almost-periodic operators with power-law long-range hopping: a Nash-Moser iteration type reducibility approach
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