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arXiv · 1804.05489

Remarks on scattering matrices for Schr\"odinger operators with critically long-range perturbations

Shu Nakamura
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Abstract

We consider scattering matrix for Schr\"odinger-type operators on $\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator, and analyze its spectrum. We present examples of which the spectrum of the scattering matrices have dense point spectrum, and absolutely continuous spectrum, respectively.

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Shu Nakamura. 2018-04-16. Remarks on scattering matrices for Schr\"odinger operators with critically long-range perturbations. https://arxiv.org/abs/1804.05489

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