The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums

R Band, O Parzanchevski, G Ben-Shach

Research output: Contribution to journalArticle (Academic Journal)peer-review

38 Citations (Scopus)

Abstract

We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For this purpose, quantum graphs are grist to the mill. We develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects. We discuss the theoretical implications which include Sunada's theorem of isospectrality (Sunada 1985 Ann. Math. 121 169) arising as a particular case of this method. A gallery of new isospectral examples is presented, and some known examples are shown to result from our theory.
Translated title of the contributionThe Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
Original languageEnglish
Pages (from-to)175202 - 175241
Number of pages42
JournalJournal of Physics A: Mathematical and Theoretical
Volume42, no 17
DOIs
Publication statusPublished - May 2009

Bibliographical note

Publisher: IOP

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