Regular quantum graphs

Details Regular quantum graphs Regular quantum graphs

2003-12-12

arxiv.org/abs/nlin/0312031v1

2004 J. Phys. A: Math. Gen. 37 6675-6686

Nonlinear Sciences

Chaotic Dynamics

12 pages, 3 figures

Scientific paper

10.1088/0305-4470/37/26/005

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.

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