Localization of the Grover Walks on Spidernets and Free Meixner Laws

Norio Konno, Nobuaki Obata, Etsuo Segawa

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the n-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.

Original languageEnglish
Pages (from-to)667-695
Number of pages29
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 2013 Sept


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