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A weak limit theorem for a class of long-range-type quantum walks in 1d

  • Kazuyuki WadaEmail author
Article

Abstract

We derive the weak limit theorem for a class of long-range-type quantum walks. To do it, we analyze spectral properties of a time evolution operator and prove that modified wave operators exist and are complete.

Keywords

Quantum walks Weak limit theorem Scattering theory 

Mathematics Subject Classification

46N50 47A40 47B47 60F05 

Notes

Acknowledgements

The author would like to thank A. Suzuki for various comments and constant encouragements. The author would also like to thank H. Ohno and S. Richard for helpful comments. This work was supported by the Research Institute of Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Institute of Technology, Hachinohe CollegeHachinoheJapan

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