Corpus ID: 207863636

Spectrum of a non-selfadjoint quantum star graph

  title={Spectrum of a non-selfadjoint quantum star graph},
  author={Gabriel Rivi{\`e}re and Julien Royer},
  • Gabriel Rivière, Julien Royer
  • Published 2019
  • Mathematics, Physics
  • We study the spectrum of a quantum star graph with a non-selfadjoint Robin condition at the central vertex. We first prove that, in the high frequency limit, the spectrum of the Robin Laplacian is close to the usual spectrum corresponding to the Kirchhoff condition. Then, we describe more precisely the asymptotics of the difference in terms of the Barra-Gaspard measure of the graph. This measure depends on the arithmetic properties of the lengths of the edges. As a by-product, this analysis… CONTINUE READING

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