Magnetic sparseness and Schr\"odinger operators on graphs

28 Nov 2017  ·  Bonnefont Michel, Golénia Sylvain, Keller Matthias, Liu Shiping, Münch Florentin ·

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. read more

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Spectral Theory Functional Analysis