• Corpus ID: 211069401

A Calder\'on type inverse problem for quantum trees

@article{Gernandt2020ACT,
  title={A Calder\'on type inverse problem for quantum trees},
  author={Hannes Gernandt and Jonathan Rohleder},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
We solve the inverse problem of recovering a metric tree from the knowledge of the Dirichlet-to-Neumann matrix on the tree's boundary corresponding to the Laplacian with standard vertex conditions. This result can be viewed as a counterpart of the Calderon problem in the analysis of PDEs; in contrast to earlier results for quantum graphs, we only assume knowledge of the Dirichlet-to-Neumann matrix for a fixed energy, not of a whole matrix-valued function. The proof is based on tracing back the… 
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