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Title: Inverse scattering problem for quantum graph vertices

Abstract

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.

Authors:
;  [1];  [2];  [3]
  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)
  3. (Czech Republic)
Publication Date:
OSTI Identifier:
21550119
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.83.062715; (c) 2011 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Cheon, Taksu, Turek, Ondrej, Exner, Pavel, and Nuclear Physics Institute ASCR, CZ-25068 Rez. Inverse scattering problem for quantum graph vertices. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.062715.
Cheon, Taksu, Turek, Ondrej, Exner, Pavel, & Nuclear Physics Institute ASCR, CZ-25068 Rez. Inverse scattering problem for quantum graph vertices. United States. doi:10.1103/PHYSREVA.83.062715.
Cheon, Taksu, Turek, Ondrej, Exner, Pavel, and Nuclear Physics Institute ASCR, CZ-25068 Rez. Wed . "Inverse scattering problem for quantum graph vertices". United States. doi:10.1103/PHYSREVA.83.062715.
@article{osti_21550119,
title = {Inverse scattering problem for quantum graph vertices},
author = {Cheon, Taksu and Turek, Ondrej and Exner, Pavel and Nuclear Physics Institute ASCR, CZ-25068 Rez},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.83.062715},
journal = {Physical Review. A},
number = 6,
volume = 83,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2011},
month = {Wed Jun 15 00:00:00 EDT 2011}
}
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