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arXiv · 1711.10418

Magnetic sparseness and Schr\"odinger operators on graphs

Michel Bonnefont·Sylvain Golénia·Matthias Keller·Shiping Liu·Florentin Münch
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Abstract

We study magnetic Schr\"odinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnetic sparse turn out to be equivalent to the fact that the form domain is an $\ell^{2}$ space. As a consequence, we get criteria of discreteness for the spectrum and eigenvalue asymptotics.

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Michel Bonnefont, Sylvain Golénia, Matthias Keller, Shiping Liu, Florentin Münch. 2017-11-28. Magnetic sparseness and Schr\"odinger operators on graphs. https://arxiv.org/abs/1711.10418

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