Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums
R. Banda, b, A. Sawickia, c and U. Smilanskyb, d
aSchool of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
bDepartment of Physics of Complex Systems, the Weizmann Institute of Science, Rehovot 76100, Israel
cCenter for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland
dCardiff School of Mathematics and WIMCS, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
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We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in the papers of Parzanchevski, Band and Ben-Shach. It was shown in the paper of Band et al. that scattering matrices of such graphs have the same spectrum and polar structure, provided that infinite leads are attached in a way which preserves the symmetry of isospectral construction. In the current paper we compare this result with the conjecture put forward by Okada et al. that the pole distribution of scattering matrices in the exterior of isospectral domains in ℝ2 is different.
DOI: 10.12693/APhysPolA.120.A-149
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