Symmetries of quantum graphs and the inverse scattering problem
(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:
https://lup.lub.lu.se/record/237635
- author
- Boman, J and Kurasov, Pavel LU
- organization
- publishing date
- 2005
- 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
- 2016-04-01 12:28:07
- date last changed
- 2022-03-29 01:19:00
@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}}, keywords = {{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}}, doi = {{10.1016/j.aam.2004.10.002}}, volume = {{35}}, year = {{2005}}, }