Simone Severini and Gregor Tanner 2004 J. Phys. A: Math. Gen. 37 6675 doi:10.1088/0305-4470/37/26/005
Regular quantum graphs
Simone Severini1 and Gregor Tanner2
Show affiliationsWe 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.
- PACS
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05.45.Mt Quantum chaos; semiclassical methods
03.67.Lx Quantum computation architectures and implementations
- MSC
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81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 26 (2 July 2004)
Received 15 December 2003, in final form 14 May 2004
Published 16 June 2004
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Regular quantum graphs
Simone Severini and Gregor Tanner 2004 J. Phys. A: Math. Gen. 37 6675
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