The dynamics of a class of quasi-periodic Schrödinger cocycles

DOI10.1007/s00023-014-0330-8zbMath1312.81061arXiv1311.5394OpenAlexW2006036491MaRDI QIDQ2339211

Kristian Bjerklöv

Publication date: 31 March 2015

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.5394

zbMATH Keywords

eigenfunctionsLyapunov exponentMorse functionquasiperiodic Schrödinger cocycle

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear difference operators (47B39) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (15)

Uniform positivity of Lyapunov exponent for a class of smooth Schrödinger cocycles with weak Liouville frequencies ⋮ On some generalizations of skew-shifts on ⋮ Must the spectrum of a random Schrödinger operator contain an interval? ⋮ The set of smooth quasi-periodic Schrödinger cocycles with positive Lyapunov exponent is not open ⋮ Sharp \(\frac{1}{2}\)-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles ⋮ Stability of the non-critical spectral properties i: arithmetic absolute continuity of the integrated density of states ⋮ Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles ⋮ A new proof of continuity of Lyapunov exponents for a class of \( C^2 \) quasiperiodic Schrödinger cocycles without LDT ⋮ Universal hierarchical structure of quasiperiodic eigenfunctions ⋮ Abundance of mode-locking for quasiperiodically forced circle maps ⋮ Continuity of the spectrum of quasi-periodic Schrödinger operators with finitely differentiable potentials ⋮ Positive Lyapunov exponent for a class of quasi-periodic cocycles ⋮ Large coupling asymptotics for the Lyapunov exponent of finitely smooth quasi-periodic Schrödinger operators ⋮ New proof of continuity of Lyapunov exponents for a class of smooth Schrödinger cocycles with weak Liouville frequencies ⋮ Uniform positivity and continuity of Lyapunov exponents for a class of \(C^2\) quasiperiodic Schrödinger cocycles

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