Regular quantum graphs.
J PHYS A-MATH GEN
6675 - 6686.
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 controlled easily. The method may find applications in the study of quantum random walks and may also prove to be useful in analysing universality in spectral statistics.
|Title:||Regular quantum graphs|
|Keywords:||PERIODIC-ORBIT THEORY, SPECTRAL STATISTICS, MATRIX|
|UCL classification:||UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
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