# Spectrum of a non-selfadjoint quantum star graph

@inproceedings{Rivire2019SpectrumOA, title={Spectrum of a non-selfadjoint quantum star graph}, author={Gabriel Rivi{\`e}re and Julien Royer}, year={2019} }

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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## On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings.

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