RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 2018, Volume 30, Issue 3, Pages 273–285 (Mi aa1604)  

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

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.

Full text: PDF file (311 kB)
First page: PDF file
References: PDF file   HTML file

Document Type: Article
Received: 30.01.2018
Language: English

Citation: H. Schanz, U. Smilansky, “Edge switching transformations of quantum graphs – a scattering approach”, Algebra i Analiz, 30:3 (2018), 273–285

Citation in format AMSBIB
\Bibitem{SchSmi18}
\by H.~Schanz, U.~Smilansky
\paper Edge switching transformations of quantum graphs~-- a~scattering approach
\jour Algebra i Analiz
\yr 2018
\vol 30
\issue 3
\pages 273--285
\mathnet{http://mi.mathnet.ru/aa1604}
\elib{http://elibrary.ru/item.asp?id=32855074}


Linking options:
  • http://mi.mathnet.ru/eng/aa1604
  • http://mi.mathnet.ru/eng/aa/v30/i3/p273

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:27
    References:4
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018