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

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

2010-08-02

arxiv.org/abs/1008.0369v2

Physics

Mathematical Physics

19 pages, 1 figure

Scientific paper

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.

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