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On isospectral potentials on periodic discrete graphs

  • Natalia Saburova
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Abstract

We consider discrete Schrödinger operators with periodic (possibly complex valued) potentials Q on periodic graphs. Using a system of spectral invariants obtained in \cite{S26}, we investigate the sets of isospectral potentials on periodic graphs. In particular, we show that the Floquet spectrum of the Schrödinger operators on the hexagonal lattice and on the Kagome lattice generically (with respect to perturbations of Q) determines the potential Q uniquely up to the obvious symmetries (translations and rotations) in the periodic graph.

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Cite

BibTeXRIS
BibTeX
@misc{saburova2026isospectral,
  title = {{On isospectral potentials on periodic discrete graphs}},
  author = {Natalia Saburova},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06820},
  eprint = {2611.06820},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06820},
}
RIS
TY  - UNPB
TI  - On isospectral potentials on periodic discrete graphs
AU  - Natalia Saburova
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06820
UR  - https://arxiv.org/abs/2611.06820
AB  - We consider discrete Schrödinger operators with periodic (possibly complex valued) potentials Q on periodic graphs. Using a system of spectral invariants obtained in \cite{S26}, we investigate the sets of isospectral potentials on periodic graphs. In particular, we show that the Floquet spectrum of the Schrödinger operators on the hexagonal lattice and on the Kagome lattice generically (with respect to perturbations of Q) determines the potential Q uniquely up to the obvious symmetries (translations and rotations) in the periodic graph.
ER  -