Construction of isoscattering non-isospectral quantum graphs using the concept of a germ graph

Abstract:The recently developed concept of germ graphs (P. Kurasov {\it et al.}, Phys. Rev. Research {\bf 7}, L022071 (2025)) is employed to construct families of isocattering, non-isospectral graphs that exhibit dissipation. More specifically, a new pair of isoscattering non-isospectral graphs is constructed by connecting the existing isoscattering non-isospectral graphs, so called attachments, to the different contact vertices of the germ graph. The existing isoscattering non-isospectral graphs contained a two-loop graph labelled $\Gamma_{A2}$ and a three-loop graph labelled $\Gamma_{A3}$. These graphs have an equal total metric length, but different topologies. The resulting graphs $\Gamma_3$ and $\Gamma_4$ are verified as non-isospectral using their Euler characteristics, while their isoscattering properties are investigated by calculating the one-port scattering matrices numerically.

arXiv:2610.13512 [quant-ph]

(or arXiv:2610.13512v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.13512 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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