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Symmetries of quantum graphs and the inverse scattering problem

Boman, J and Kurasov, Pavel LU (2005) In Advances in Applied Mathematics 35(1). p.58-70
Abstract
The Schrodinger equation on a graph together with a set of self-adjoint boundary conditions at the vertices determine a quantum graph. If the graph has one or more infinite edges one can associate a scattering matrix to the quantum graph. It is proved that if such a graph has internal symmetries then the boundary conditions, and hence the self-adjoint operator describing the quantum system, in general cannot be reconstructed from the scattering matrix. In addition it is shown that if the Schrodinger operator possesses internal symmetry then there exists a different quantum graph associated with the same scattering matrix.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
inverse scattering problem, quantum graph, schrodinger operator
in
Advances in Applied Mathematics
volume
35
issue
1
pages
58 - 70
publisher
Elsevier
external identifiers
  • wos:000229709500004
  • scopus:19144361977
ISSN
1090-2074
DOI
10.1016/j.aam.2004.10.002
language
English
LU publication?
yes
id
a6c2ccbe-57d6-42d6-8fe5-734c6bed2251 (old id 237635)
date added to LUP
2007-08-24 12:05:48
date last changed
2017-11-05 03:46:26
@article{a6c2ccbe-57d6-42d6-8fe5-734c6bed2251,
  abstract     = {The Schrodinger equation on a graph together with a set of self-adjoint boundary conditions at the vertices determine a quantum graph. If the graph has one or more infinite edges one can associate a scattering matrix to the quantum graph. It is proved that if such a graph has internal symmetries then the boundary conditions, and hence the self-adjoint operator describing the quantum system, in general cannot be reconstructed from the scattering matrix. In addition it is shown that if the Schrodinger operator possesses internal symmetry then there exists a different quantum graph associated with the same scattering matrix.},
  author       = {Boman, J and Kurasov, Pavel},
  issn         = {1090-2074},
  keyword      = {inverse scattering problem,quantum graph,schrodinger operator},
  language     = {eng},
  number       = {1},
  pages        = {58--70},
  publisher    = {Elsevier},
  series       = {Advances in Applied Mathematics},
  title        = {Symmetries of quantum graphs and the inverse scattering problem},
  url          = {http://dx.doi.org/10.1016/j.aam.2004.10.002},
  volume       = {35},
  year         = {2005},
}