Non-existence of standard wave operators for fractional laplacian and slowly decaying potentials

Atsuhide Ishida

doi:10.4208/eajam.230418.170918

Non-existence of standard wave operators for fractional laplacian and slowly decaying potentials

Atsuhide Ishida

葛飾キャンパス教養部

研究成果: Article › 査読

4 被引用数 (Scopus)

抄録

Quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials are considered. If the potential function slowly decays and the Dollard-type modified wave operators exist and are asymptotically complete, we prove that the factional Laplacian does not possess the standard wave operators. This result suggests the borderline between the short- and long-range behaviour.

本文言語	English
ページ（範囲）	233-240
ページ数	8
ジャーナル	East Asian Journal on Applied Mathematics
巻	9
号	2
DOI	https://doi.org/10.4208/eajam.230418.170918
出版ステータス	Published - 5月 2019

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title = "Non-existence of standard wave operators for fractional laplacian and slowly decaying potentials",

abstract = "Quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials are considered. If the potential function slowly decays and the Dollard-type modified wave operators exist and are asymptotically complete, we prove that the factional Laplacian does not possess the standard wave operators. This result suggests the borderline between the short- and long-range behaviour.",

author = "Atsuhide Ishida",

note = "Funding Information: This work was partially supported by the Grant-in-Aid for Young Scientists (B) from the JSPS (#16K17633). Publisher Copyright: {\textcopyright} 2019 Global-Science Press.",

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AB - Quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials are considered. If the potential function slowly decays and the Dollard-type modified wave operators exist and are asymptotically complete, we prove that the factional Laplacian does not possess the standard wave operators. This result suggests the borderline between the short- and long-range behaviour.

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Non-existence of standard wave operators for fractional laplacian and slowly decaying potentials

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