Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials

Abstract

We give a criterion implying subcritical behavior for quasi-periodic Schrödinger operators where the potential sampling function is given by a trigonometric polynomial. Subcritical behavior, in the sense of Avila's global theory, is known to imply purely absolutely continuous spectrum for all irrational frequencies and all phases.

arXiv commentto appear in the Journal of Spectral Theory

References in corpus (8)

• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Complex one-frequency cocycles
• Almost reducibility and absolute continuity I
• Continuity of the Lyapunov Exponent for analytic quasi-perodic cocycles with singularities
• Global theory of one-frequency Schrodinger operators I: stratified analyticity of the Lyapunov exponent and the boundary of nonuniform hyperbolicity
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Cited by in corpus (2)

• A lower bound on the Lyapunov exponent for the generalized Harper's model
• Large coupling asymptotics for the Lyapunov exponent of quasi-periodic Schrödinger operators with analytic potentials