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arXiv · 1709.05614

Continuous quasiperiodic Schrödinger operators with Gordon type potentials

Wencai Liu
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Abstract

Let us concern the quasi-periodic Schrödinger operator in the continuous case, \begin{equation*} (Hy)(x)=-y^{\prime\prime}(x)+V(x,ωx)y(x), \end{equation*} where $V:(\R/\Z)^2\to \R$ is piecewisely $γ$-Hölder continuous with respect to the second variable. Let $L(E)$ be the Lyapunov exponent of $Hy=Ey$. Define $β(ω)$ as \begin{equation*} β(ω)= \limsup_{k\to \infty}\frac{-\ln ||kω||}{k}. \end{equation*} We prove that $H$ admits no eigenvalue in regime $\{E\in\R:L(E)<γβ(ω)\}$.

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Wencai Liu. 2018-08-23. Continuous quasiperiodic Schrödinger operators with Gordon type potentials. https://doi.org/10.1063/1.5005076

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