Inverse scattering problem for quantum graph vertices

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.062715· OSTI ID:21550119

Cheon, Taksu; Turek, Ondrej ^[1]; Exner, Pavel ^[2]

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1. Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502 (Japan)
2. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Brehova 7, CZ-11519 Prague (Czech Republic)

We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.

• OSTI ID: 21550119
• Journal Information: Physical Review. A, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevA.83.062715; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
COUPLING
GRAPH THEORY
INVERSE SCATTERING PROBLEM
PROBABILITY
QUANTUM STATES
SCALE INVARIANCE
TRANSMISSION
UNITARITY
VORTICES
INVARIANCE PRINCIPLES
MATHEMATICS