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Commutator Methods for N-Body Schrödinger Operators

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Spectral Theory and Mathematical Physics

Part of the book series: Latin American Mathematics Series ((LAMSUFSC))

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Abstract

This is a short report on the authors’ recent work on spectral theory of N-body Schrödinger operators (Adachi et al., New Methods in Spectral Theory of N-Body Schrodinger Operators, arXiv:1804.07874 [math-ph]). We present Rellich’s theorem, the limiting absorption principle, microlocal resolvent bounds, and a microlocal Sommerfeld uniqueness result. Our assumptions on pair-potentials are minimal: Each of them consists 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. In addition, our setup also allows hard-core interactions. The proofs depend on a commutator scheme recently proposed by two of the authors (Ito and Skibsted, J. Funct. Anal. 278(9), 108449 (2020)).

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Acknowledgements

K. Ito would like to thank the anonymous referee for valuable comments that improved presentation of this paper. T.A. is supported by JSPS KAKENHI, grant nr. 17K05319. K. Ito is supported by JSPS KAKENHI, grant nr. 17K05325. E.S. is supported by the Danish Council for Independent Research | Natural Sciences, grant nr. DFF-4181-00042.

Author information

Authors and Affiliations

  1. Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan

    Tadayoshi Adachi

  2. Research Organization of Science and Technology, Ritsumeikan University, Shiga, Japan

    Kyohei Itakura

  3. Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan

    Kenichi Ito

  4. Institut for Matematiske Fag, Aarhus Universitet, Aarhus C, Denmark

    Erik Skibsted

Authors
  1. Tadayoshi Adachi
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  2. Kyohei Itakura
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  3. Kenichi Ito
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  4. Erik Skibsted
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Corresponding author

Correspondence to Kenichi Ito .

Editor information

Editors and Affiliations

  1. Departamento de Matemáticas y C. C., Universidad de Santiago de Chile, Santiago, Chile

    Pablo Miranda

  2. Institut de Mathématiques de Bordeaux, Talence, Gironde, France

    Nicolas Popoff

  3. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Georgi Raikov

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Adachi, T., Itakura, K., Ito, K., Skibsted, E. (2020). Commutator Methods for N-Body Schrödinger Operators. In: Miranda, P., Popoff, N., Raikov, G. (eds) Spectral Theory and Mathematical Physics. Latin American Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-55556-6_1

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