Absence of wave operators for one-dimensional quantum walks

  • Kazuyuki WadaEmail author


We show that there exist pairs of two time evolution operators which do not have wave operators in a context of one-dimensional discrete time quantum walks. As a consequence, the borderline between existence and nonexistence of wave operators is decided.


Scattering theory Wave operator Quantum walk 

Mathematics Subject Classification

46N50 47A40 



The author thanks the referee for useful comments.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.National Institute of TechnologyHachinohe CollegeHachinoheJapan

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