Scattering from isospectral quantum graphs

TL;DR

This paper investigates scattering properties of isospectral quantum graphs, revealing that certain extensions have conjugate scattering matrices with identical pole distributions, providing new insights into their spectral characteristics.

Contribution

It demonstrates that for specific extensions, isospectral quantum graphs have conjugate scattering matrices and identical pole distributions, connecting isospectral theory with scattering analysis.

Findings

Scattering matrices of certain isospectral graphs are conjugate.

Poles of scattering matrices are identical for these graphs.

Provides new insights into isospectral construction via scattering approach.

Abstract

Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles distributions are therefore identical. The scattering matrices are studied using a recently developed isospectral theory. At the same time, the scattering approach offers a new insight on the mentioned isospectral construction.