Quantum graph walks II: Quantum walks on graph coverings
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 Lfunction 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 Lfunctions. As an application, we introduce three types of quantum graph walks, and treat their relation.
 Publication:

arXiv eprints
 Pub Date:
 November 2012
 arXiv:
 arXiv:1211.4719
 Bibcode:
 2012arXiv1211.4719H
 Keywords:

 Mathematical Physics;
 Mathematics  Combinatorics;
 81Q10;
 05C50;
 05C60;
 81P68
 EPrint:
 27 page, 2 figures