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Spin Chains, Graphs and State Revival

  • Hiroshi Miki
  • Satoshi Tsujimoto
  • Luc VinetEmail author
Conference paper
  • 47 Downloads
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

Abstract

Connections between the 1-excitation dynamics of spin lattices and quantum walks on graphs will be surveyed. Attention will be paid to perfect state transfer (PST) and fractional revival (FR) as well as to the role played by orthogonal polynomials in the study of these phenomena. Included is a discussion of the ordered Hamming scheme, its relation to multivariate Krawtchouk polynomials of the Tratnik type, the exploration of quantum walks on graphs of this association scheme and their projection to spin lattices with PST and FR.

Keywords

Quantum walk Quantum State transfer Orthogonal polynomials 

Mathematics Subject Classification (2000)

Primary 33C45; Secondary 81R30 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Meteorological CollegeAsahi-Cho, KashiwaJapan
  2. 2.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversitySakyo-KuJapan
  3. 3.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada

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