Localization of the Grover Walks on Spidernets and Free Meixner Laws

@article{Konno2013LocalizationOT,
title={Localization of the Grover Walks on Spidernets and Free Meixner Laws},
author={N. Konno and N. Obata and E. Segawa},
journal={Communications in Mathematical Physics},
year={2013},
volume={322},
pages={667-695}
}

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… CONTINUE READING