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Inverse problems for Aharonov–Bohm rings

Published online by Cambridge University Press:  26 November 2009

P. KURASOV
P. KURASOV*
Affiliation:
Department of Mathematics, LTH, Lund University, Box 118, 221 00 Lund, Sweden Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden Department of Physics, St Petersburg University, 198904 St. Peterhof, Russia. e-mail: kurasov@maths.lth.se
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Abstract

The inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It is shown that the knowledge of the Titchmarsh–Weyl matrix function (Dirichlet-to-Neumann map) for just two values of the magnetic field allows one to reconstruct the graph and potential on it provided a certain additional no-resonance condition is satisfied.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 2 , March 2010 , pp. 331 - 362
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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