Spectrum of a nonselfadjoint quantum star graph
Abstract
We study the spectrum of a quantum star graph with a nonselfadjoint 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 BarraGaspard measure of the graph. This measure depends on the arithmetic properties of the lengths of the edges. As a byproduct, this analysis provides a Weyl Law for nonselfadjoint quantum star graphs and it gives the asymptotic behaviour of the imaginary parts of the eigenvalues.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.04760
 Bibcode:
 2019arXiv191104760R
 Keywords:

 Mathematical Physics;
 Mathematics  Spectral Theory