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Letters in Mathematical Physics

, Volume 109, Issue 1, pp 61–88 | Cite as

Quantum walks with an anisotropic coin II: scattering theory

  • S. Richard
  • A. Suzuki
  • R. Tiedra de Aldecoa
Article

Abstract

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.

Keywords

Quantum walks Unitary operators Scattering theory Weak limit theorem 

Mathematics Subject Classification

46N50 47A40 47B47 60F05 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityChikusa-ku, NagoyaJapan
  2. 2.Division of Mathematics and Physics, Faculty of EngineeringShinshu UniversityWakasato, NaganoJapan
  3. 3.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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