Opening gaps in the spectrum of strictly ergodic Schrödinger operators

DOI10.4171/JEMS/296zbMath1263.37007arXiv0903.2281MaRDI QIDQ653288

Artur Avila, David Damanik, Jairo Bochi

Publication date: 9 January 2012

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.2281

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Ergodic theory of linear operators (47A35) Ergodicity, mixing, rates of mixing (37A25) Spectrum, resolvent (47A10) Schrödinger operator, Schrödinger equation (35J10) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Lattice dynamics; integrable lattice equations (37K60)

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Cites Work

• Unnamed Item
• Cantor spectrum for Schrödinger operators with potentials arising from generalized skew-shifts
• Some aspects of the theory of asymptotic cycles
• The Ten Martini problem
• Weak mixing for interval exchange transformations and translation flows
• A uniform dichotomy for generic ${\rm SL}(2,{\mathbb{R}})$ cocycles over a minimal base

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