Subcritical behavior for quasi-periodic Schrödinger cocycles with trigonometric potentials

2015/09/17 by Christoph A. Marx, C. A. Marx, Marx, C. A. +6
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1509.05279

to appear in the Journal of Spectral Theory

openalex publication_date 2015/09/17 · arxiv created 2015/10/31 · arxiv updated 2015/11/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Global theory of one-frequency Schrodinger operators I: stratified analyticity of the Lyapunov exponent and the boundary of nonuniform hyperbolicity
• Hölder continuity of Lyapunov exponent for quasi-periodic Jacobi operators
• Almost reducibility and absolute continuity I
• Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators

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