Regular quantum graphs

Abstract

We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way incoming and outgoing channels at vertex scattering processes are connected. Symmetry properties of the quantum graph as well as its spectral statistics depend on the particular choice of permutation matrices, also called connectivity matrices, and can now be easily controlled. The method may find applications in the study of quantum random walks networks and may also prove to be useful in analysing universality in spectral statistics.

12 pages, 3 figures

References in corpus (2)

• Quantum random walks - an introductory overview
• On the digraph of a unitary matrix

Cited by in corpus (9)

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• Green's function approach for quantum graphs: an overview
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• From quantum graphs to quantum random walks
• Well-Posedness and Symmetries of Strongly Coupled Network Equations
• Zero forcing in iterated line digraphs
• Graphs of unitary matrices
• Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs
• Quantum graph walks II: Quantum walks on graph coverings