Singular continuous spectrum for singular potential

Svetlana Jitomirskaya; Fan Yang

doi:10.1007/s00220-016-2823-4

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arXiv · 1604.04907

Singular continuous spectrum for singular potential

Svetlana Jitomirskaya·Fan Yang

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Abstract

We prove that Schrödinger operators with meromorphic potentials $(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ \frac{g(θ+nα)}{f(θ+nα)} u_n$ have purely singular continuous spectrum on the set $\{E: L(E)<δ{(α,θ)}\}$, where $δ$ is an explicit function, and $L$ is the Lyapunov exponent. This extends results of Jitomirskaya and Liu for the Maryland model and of Avila, You and Zhou for the almost Mathieu operator, to the general family of meromorphic potentials.

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BibTeX RIS

Svetlana Jitomirskaya, Fan Yang. 2016-04-17. Singular continuous spectrum for singular potential. https://doi.org/10.1007/s00220-016-2823-4

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