The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
Mathematical Physics
2009-11-13 v2 math.MP
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 that 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 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.
Keywords
Cite
@article{arxiv.0812.2282,
title = {The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums},
author = {Ram Band and Ori Parzanchevski and Gilad Ben-Shach},
journal= {arXiv preprint arXiv:0812.2282},
year = {2009}
}