Edge switching transformations of quantum graphs – a scattering approach
H. Schanza, U. Smilanskyb
a Institute of Mechanical Engineering, University of Applied Sciences Magdeburg-Stendal, D-39114 Magdeburg, Germany
b Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
Some elementary transformations of quantum graphs are discussed and their effects on the spectra of the Schrödinger operators are studied. In particular, the edge swapping operation is considered, where the lengths of two edges are interchanged, as well as switching, where the connectivity of the graph is modified by reconnecting two edges. Both transformations preserve the total length of the graphs. This problem was already studied at length and in generality in a previous paper. Here, it is addressed from a different viewpoint based on a scattering approach, yielding a trace formula for the difference between the spectral counting functions before and after the transformation.
Schrödinger operator, quantum graph, length swapping, edge switching.
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H. Schanz, U. Smilansky, “Edge switching transformations of quantum graphs – a scattering approach”, Algebra i Analiz, 30:3 (2018), 273–285
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\by H.~Schanz, U.~Smilansky
\paper Edge switching transformations of quantum graphs~-- a~scattering approach
\jour Algebra i Analiz
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