On the spectrum of lattice Schrödinger operators with deterministic potential. II.

DOI10.1007/BF02786578zbMath1058.47002OpenAlexW4243054343MaRDI QIDQ1411686

Jean Bourgain

Publication date: 15 December 2003

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02786578

zbMATH Keywords

absolutely continuous spectrumexistence of spectral gapsone-dimensional lattice Schrödinger operators

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Statistical mechanics of solids (82D20) Linear difference operators (47B39)

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Cites Work

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• Absolutely continuous spectrum for 1D quasiperiodic operators.
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• Methods of KAM-theory for long-range quasi-periodic operators on \({\mathbb{Z}}^{\nu}\). Pure point spectrum
• On the spectrum of lattice Schrödinger operators with deterministic potential
• Anderson localization for the 1-D discrete Schrödinger operator with two-frequency potential
• Metal-insulator transition for the almost Mathieu operator
• On nonperturbative localization with quasi-periodic potential.
• Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions

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