SchrÖdinger operators with guided potentials on periodic graphs

Evgeny Korotyaev, Наталья Сабурова

Research output

4 Citations (Scopus)

Abstract

We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided non-positive potentials, which are periodic in some directions and finitely supported in other ones. The spectrum of the unperturbed operator is a union of a finite number of non-degenerate bands and eigenvalues of infinite multiplicity. We show that the spectrum of the perturbed operator consists of the “unperturbed” one plus the additional guided spectrum, which is a union of a finite number of bands. We estimate the position of the guided bands and their length in terms of graph geometric parameters. We also determine the asymptotics of the guided bands for large guided potentials. Moreover, we show that the possible number of the guided bands, their length and position can be rather arbitrary for some specific potentials.

Original languageEnglish
Pages (from-to)4869-4883
Number of pages15
JournalProceedings of the American Mathematical Society
Volume145
Issue number11
DOIs
Publication statusPublished - 1 Jan 2017

Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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