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New methods in spectral theory of N -body Schrödinger operators

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New methods in spectral theory of N -body Schrödinger operators. / Adachi, T.; Itakura, K.; Ito, K. et al.
In: Reviews in Mathematical Physics, Vol. 33, No. 5, 2150015, 06.2021.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Harvard

Adachi, T, Itakura, K, Ito, K & Skibsted, E 2021, 'New methods in spectral theory of N -body Schrödinger operators', Reviews in Mathematical Physics, vol. 33, no. 5, 2150015. https://doi.org/10.1142/S0129055X2150015X

APA

Adachi, T., Itakura, K., Ito, K., & Skibsted, E. (2021). New methods in spectral theory of N -body Schrödinger operators. Reviews in Mathematical Physics, 33(5), Article 2150015. https://doi.org/10.1142/S0129055X2150015X

CBE

Adachi T, Itakura K, Ito K, Skibsted E. 2021. New methods in spectral theory of N -body Schrödinger operators. Reviews in Mathematical Physics. 33(5):Article 2150015. https://doi.org/10.1142/S0129055X2150015X

MLA

Adachi, T. et al. "New methods in spectral theory of N -body Schrödinger operators". Reviews in Mathematical Physics. 2021. 33(5). https://doi.org/10.1142/S0129055X2150015X

Vancouver

Adachi T, Itakura K, Ito K, Skibsted E. New methods in spectral theory of N -body Schrödinger operators. Reviews in Mathematical Physics. 2021 Jun;33(5):2150015. doi: 10.1142/S0129055X2150015X

Author

Adachi, T. ; Itakura, K. ; Ito, K. et al. / New methods in spectral theory of N -body Schrödinger operators. In: Reviews in Mathematical Physics. 2021 ; Vol. 33, No. 5.

Bibtex

@article{71da19f31fea4c86adc51599af216467,
title = "New methods in spectral theory of N -body Schr{\"o}dinger operators",
abstract = "We develop a new scheme of proofs for spectral theory of the N-body Schr{\"o}dinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, H{\"o}lder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.",
keywords = "minimal non-threshold generalized eigenfunctions, N -body Schr{\"o}dinger operators",
author = "T. Adachi and K. Itakura and K. Ito and E. Skibsted",
note = "Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",
year = "2021",
month = jun,
doi = "10.1142/S0129055X2150015X",
language = "English",
volume = "33",
journal = "Reviews in Mathematical Physics",
issn = "0129-055X",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "5",

}

RIS

TY - JOUR

T1 - New methods in spectral theory of N -body Schrödinger operators

AU - Adachi, T.

AU - Itakura, K.

AU - Ito, K.

AU - Skibsted, E.

N1 - Publisher Copyright: © 2021 World Scientific Publishing Company.

PY - 2021/6

Y1 - 2021/6

N2 - We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.

AB - We develop a new scheme of proofs for spectral theory of the N-body Schrödinger operators, reproducing and extending a series of sharp results under minimum conditions. Our main results include Rellich's theorem, limiting absorption principle bounds, microlocal resolvent bounds, Hölder continuity of the resolvent and a microlocal Sommerfeld uniqueness result. We present a new proof of Rellich's theorem which is unified with exponential decay estimates studied previously only for L2-eigenfunctions. Each pair-potential is a sum of a long-range term with first-order derivatives, a short-range term without derivatives and a singular term of operator- or form-bounded type, and the setup includes hard-core interaction. Our proofs consist of a systematic use of commutators with 'zeroth order' operators. In particular, they do not rely on Mourre's differential inequality technique.

KW - minimal non-threshold generalized eigenfunctions

KW - N -body Schrödinger operators

UR - http://www.scopus.com/inward/record.url?scp=85100492756&partnerID=8YFLogxK

U2 - 10.1142/S0129055X2150015X

DO - 10.1142/S0129055X2150015X

M3 - Journal article

AN - SCOPUS:85100492756

VL - 33

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 5

M1 - 2150015

ER -