Spectra of Schroedinger operators on equilateral quantum graphs

Details Spectra of Schroedinger operators on equilateral quantum graphs Spectra of Schroedinger operators on equilateral quantum graphs

2005-12-28

arxiv.org/abs/math-ph/0512090v2

Lett. Math. Phys. 77 (2006) 139-154, available on www.springeronline.com (see DOI)

Physics

Mathematical Physics

14 pages: content reorganized, typos corrected

Scientific paper

10.1007/s11005-006-0088-0

We consider magnetic Schroedinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, it is shown that the spectrum on the quantum graph is the preimage of the combinatorial spectrum under a certain entire function. Using this correspondence we show that that the number of gaps in the spectrum of the Schroedinger operators admits an estimate from below in terms of the Hill operator independently of the graph structure.

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