Quantum graph walks II: Quantum walks on graph coverings
Mathematical Physics
2012-11-21 v1 Combinatorics
math.MP
Abstract
We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the characteristic polynomial of the bond scattering matrix of a regular covering of G by means of its L-functions. As an application, we introduce three types of quantum graph walks, and treat their relation.
Cite
@article{arxiv.1211.4719,
title = {Quantum graph walks II: Quantum walks on graph coverings},
author = {Yusuke Higuchi and Norio Konno and Iwao Sato and Etsuo Segawa},
journal= {arXiv preprint arXiv:1211.4719},
year = {2012}
}
Comments
27 page, 2 figures