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- W3100623591 abstract "We consider normalized Laplacians and their perturbations by periodic potentials (Schrodinger operators) on periodic discrete graphs. The spectrum of the operators consists of an absolutely continuous part (a union of a finite number of non-degenerate bands) and a finite number of flat bands, i.e., eigenvalues of infinite multiplicity. We obtain estimates of the Lebesgue measure of the spectrum in terms of geometric parameters of the graphs and show that they become identities for some class of graphs. We determine two-sided estimates on the length of the first spectral band and on the effective mass at the bottom of the spectrum of the Laplace and Schrodinger operators. In particular, these estimates yield that the first spectral band of Schrodinger operators is non-degenerate." @default.
- W3100623591 created "2020-11-23" @default.
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- W3100623591 date "2019-06-04" @default.
- W3100623591 modified "2023-10-16" @default.
- W3100623591 title "Spectral estimates for Schrödinger operators on periodic discrete graphs" @default.
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- W3100623591 doi "https://doi.org/10.1090/spmj/1565" @default.
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