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Mathematical Physics

arXiv:1804.05489 (math-ph)
[Submitted on 16 Apr 2018 (v1), last revised 24 Mar 2020 (this version, v6)]

Title:Remarks on scattering matrices for Schrödinger operators with critically long-range perturbations

Authors:Shu Nakamura
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Abstract:We consider scattering matrix for Schrödinger-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.
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: 58J50, 35P25, 81U05
Cite as: arXiv:1804.05489 [math-ph]
  (or arXiv:1804.05489v6 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1804.05489

Submission history

From: Shu Nakamura [view email]
[v1] Mon, 16 Apr 2018 03:14:45 UTC (13 KB)
[v2] Wed, 18 Apr 2018 01:31:05 UTC (13 KB)
[v3] Thu, 19 Apr 2018 02:06:10 UTC (8 KB)
[v4] Fri, 27 Apr 2018 06:05:12 UTC (16 KB)
[v5] Sun, 18 Nov 2018 02:40:53 UTC (16 KB)
[v6] Tue, 24 Mar 2020 05:32:27 UTC (16 KB)
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