Nodal domains on isospectral quantum graphs: the resolution of isospectrality ?
Chaotic Dynamics
2009-11-11 v3 Mathematical Physics
math.MP
Abstract
We present and discuss isospectral quantum graphs which are not isometric. These graphs are the analogues of the isospectral domains in R2 which were introduced recently and are all based on Sunada's construction of isospectral domains. After presenting some of the properties of these graphs, we discuss a few examples which support the conjecture that by counting the nodal domains of the corresponding eigenfunctions one can resolve the isospectral ambiguity.
Cite
@article{arxiv.nlin/0608031,
title = {Nodal domains on isospectral quantum graphs: the resolution of isospectrality ?},
author = {Ram Band and Talia Shapira and Uzy Smilansky},
journal= {arXiv preprint arXiv:nlin/0608031},
year = {2009}
}