期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
卷 34, 期 31, 页码 6061-6068出版社
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/34/31/301
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We show that the spectrum of the Schrodinger operator on a finite, metric graph determines uniquely the connectivity matrix and the bond lengths, provided that the lengths are non-commensurate and the connectivity is simple (no parallel bonds between vertices and no loops connecting a vertex to itself). That is, one can hear the shape of the graph! We also consider a related inversion problem: a compact graph can be converted into a scattering system by attaching to its vertices leads to infinity. We show that the scattering phase determines uniquely the compact part of the graph, under similar conditions as above.
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