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 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.

27 page, 2 figures

References in corpus (8)

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• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Functionals of the Brownian motion, localization and metric graphs
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• From quantum graphs to quantum random walks
• Spectral determinant on graphs with generalized boundary conditions
• Regular quantum graphs
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