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Aharonov-Bohm Ring Touching A Quantum Wire: How To Model It And To Solve The Inverse Problem

Kurasov, Pavel LU and Enerback, Magnus (2011) In Reports on Mathematical Physics 68(3). p.271-287
Abstract
An explicitly solvable model of the gated Aharonov-Bohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the Titchmarsh-Weyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
quantum graphs, inverse problems
in
Reports on Mathematical Physics
volume
68
issue
3
pages
271 - 287
publisher
Elsevier
external identifiers
  • wos:000299755800003
  • scopus:84857588690
ISSN
0034-4877
DOI
10.1016/S0034-4877(12)60010-X
language
English
LU publication?
yes
id
cd53da0c-9a2b-43ed-b56f-1fe3475fb37f (old id 2378606)
alternative location
http://www2.math.su.se/~pak/PDFARCHIV/2011-RMP.pdf
date added to LUP
2016-04-01 10:46:16
date last changed
2025-10-14 13:15:33
@article{cd53da0c-9a2b-43ed-b56f-1fe3475fb37f,
  abstract     = {{An explicitly solvable model of the gated Aharonov-Bohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the Titchmarsh-Weyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.}},
  author       = {{Kurasov, Pavel and Enerback, Magnus}},
  issn         = {{0034-4877}},
  keywords     = {{quantum graphs; inverse problems}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{271--287}},
  publisher    = {{Elsevier}},
  series       = {{Reports on Mathematical Physics}},
  title        = {{Aharonov-Bohm Ring Touching A Quantum Wire: How To Model It And To Solve The Inverse Problem}},
  url          = {{http://dx.doi.org/10.1016/S0034-4877(12)60010-X}},
  doi          = {{10.1016/S0034-4877(12)60010-X}},
  volume       = {{68}},
  year         = {{2011}},
}