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arXiv · 1406.7523

Spectral band bracketing for Laplacians on periodic metric graphs

Evgeny Korotyaev·Natalia Saburova
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Abstract

We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite number of flat bands, i.e., eigenvalues of infinite multiplicity. Our main result is a localization of spectral bands in terms of eigenvalues of Dirichlet and Neumann operators on a fundamental domain of the periodic graph. The proof is based on the spectral band localization for discrete Laplacians and on the relation between the spectra of discrete and metric Laplacians.

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Evgeny Korotyaev, Natalia Saburova. 2014-06-29. Spectral band bracketing for Laplacians on periodic metric graphs. https://arxiv.org/abs/1406.7523

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