Magnetic Schrödinger operators on periodic discrete graphs

Evgeny Korotyaev, Наталья Сабурова

Research output

10 Citations (Scopus)

Abstract

We consider magnetic Schrödinger operators with periodic magnetic and electric potentials 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) plus a finite number of flat bands, i.e., eigenvalues of infinite multiplicity. We estimate the Lebesgue measure of the spectrum in terms of the Betti numbers and show that these estimates become identities for specific graphs. We estimate a variation of the spectrum of the Schrödinger operators under a perturbation by a magnetic field in terms of magnetic fluxes. The proof is based on Floquet theory and a precise representation of fiber magnetic Schrödinger operators constructed in the paper.

Original languageEnglish
Pages (from-to)1625-1660
Number of pages36
JournalJournal of Functional Analysis
Volume272
Issue number4
DOIs
Publication statusPublished - 15 Feb 2017

Scopus subject areas

  • Analysis

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