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Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 273–285 (Mi aa1604)  
This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

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
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Abstract: 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.
Keywords: Schrödinger operator, quantum graph, length swapping, edge switching.
Received: 30.01.2018
English version:
St. Petersburg Mathematical Journal, 2019, Volume 30, Issue 3, Pages 591–600
DOI: https://doi.org/10.1090/spmj/1560
Bibliographic databases:
Document Type: Article
Language: English
Citation: H. Schanz, U. Smilansky, “Edge switching transformations of quantum graphs – a scattering approach”, Algebra i Analiz, 30:3 (2018), 273–285; St. Petersburg Math. J., 30:3 (2019), 591–600
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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