Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

Gregory Berkolaiko, Peter Kuchment

Type: Other

Publication Date: 2012-01-01

Citations: 50

DOI: https://doi.org/10.1090/pspum/084/1352

Abstract

We study the dependence of the quantum graph Hamiltonian, its resolvent, and its spectrum on the vertex conditions and graph edge lengths. In particular, several results on the interlacing (bracketing) of the spectra of graphs with different vertex conditions are obtained and their applications are discussed.

Locations

Proceedings of symposia in pure mathematics - View
arXiv (Cornell University) - PDF

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