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Spin Chains, Graphs and State Revival

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Orthogonal Polynomials (AIMSVSW 2018)

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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.

The research of ST is supported by JSPS KAKENHI (Grant Numbers 16K13761) and that of LV by a discovery grant of the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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Author information

Authors and Affiliations

  1. Meteorological College, Asahi-Cho, Kashiwa, Japan

    Hiroshi Miki

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Sakyo-Ku, Kyoto, Japan

    Satoshi Tsujimoto

  3. Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada

    Luc Vinet

Authors
  1. Hiroshi Miki
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  2. Satoshi Tsujimoto
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  3. Luc Vinet
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Corresponding author

Correspondence to Luc Vinet .

Editor information

Editors and Affiliations

  1. University of Yaoundé I, Yaoundé, Cameroon; African Institute for Mathematical Sciences, Limbe, Cameroon

    Mama Foupouagnigni

  2. Institute for Mathematics, University of Kassel, Kassel, Germany

    Wolfram Koepf

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Miki, H., Tsujimoto, S., Vinet, L. (2020). Spin Chains, Graphs and State Revival. In: Foupouagnigni, M., Koepf, W. (eds) Orthogonal Polynomials. AIMSVSW 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36744-2_20

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