Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on $\mathbb{R}^d$

Yunfeng Shi

doi:10.1007/s00220-021-04174-z

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arXiv · 2006.11925

Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on $\mathbb{R}^d$

Yunfeng Shi

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Abstract

In this paper we study on $L^2(\mathbb{R}^d)$ the quasi-periodic Schr\"odinger operator $H=-\Delta+ \lambda V(x),$ where $V$ is a real analytic quasi-periodic function and $\lambda>0$. We first show that $H$ has no eigenvalues in \textit{low energy region}. We also provide in \textit{low energy region} the new phase transition parameter, i.e. the competition between the strength of coupling and the length for frequencies.

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BibTeX RIS

Yunfeng Shi. 2020-06-21. Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on $\mathbb{R}^d$. https://doi.org/10.1007/s00220-021-04174-z

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