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Mathematical Physics

arXiv:1903.00145 (math-ph)
[Submitted on 1 Mar 2019]

Title:Spin Chains, Graphs and State Revival

Authors:Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
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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.
Comments: 20 pages, based on the lecture delivered by Luc Vinet at the AIMS-Volkwagen workshop 2018 in Douala, Cameroun
Subjects: Mathematical Physics (math-ph)
MSC classes: 81P45, 33C45, 05E30
Cite as: arXiv:1903.00145 [math-ph]
  (or arXiv:1903.00145v1 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1903.00145

Submission history

From: Luc Vinet [view email]
[v1] Fri, 1 Mar 2019 03:45:55 UTC (579 KB)
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