The isospectral fruits of representation theory: Quantum graphs and drums

Ram Band*, Ori Parzanchevski, Gilad Ben-Shach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

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.

Original languageAmerican English
Article number175202
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number17
DOIs
StatePublished - 2009

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