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PreprintCC BY 4.0arXiv

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

  • Omer Farooq
  • Michał Ławniczak
  • Leszek Sirko
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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 ΓA2 and a three-loop graph labelled ΓA3. These graphs have an equal total metric length, but different topologies. The resulting graphs Γ3 and Γ4 are verified as non-isospectral using their Euler characteristics, while their isoscattering properties are investigated by calculating the one-port scattering matrices numerically.

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Cite

BibTeXRIS
BibTeX
@misc{farooq2026construction,
  title = {{Construction of isoscattering non-isospectral quantum graphs using the concept of a germ graph}},
  author = {Omer Farooq and Michał Ławniczak and Leszek Sirko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13512},
  eprint = {2610.13512},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13512},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Construction of isoscattering non-isospectral quantum graphs using the concept of a germ graph
AU  - Omer Farooq
AU  - Michał Ławniczak
AU  - Leszek Sirko
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13512
UR  - https://arxiv.org/abs/2610.13512
AB  - 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 Γ_A2 and a three-loop graph labelled Γ_A3. These graphs have an equal total metric length, but different topologies. The resulting graphs Γ_3 and Γ_4 are verified as non-isospectral using their Euler characteristics, while their isoscattering properties are investigated by calculating the one-port scattering matrices numerically.
ER  -