Magnetic Schrödinger operators on periodic discrete graphs

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Magnetic Schrödinger operators on periodic discrete graphs. / Korotyaev, Evgeny; Сабурова, Наталья.

In: Journal of Functional Analysis, Vol. 272, No. 4, 15.02.2017, p. 1625-1660.

Research output: Contribution to journal › Article › peer-review

Author

Korotyaev, Evgeny ; Сабурова, Наталья. / Magnetic Schrödinger operators on periodic discrete graphs. In: Journal of Functional Analysis. 2017 ; Vol. 272, No. 4. pp. 1625-1660.

BibTeX

@article{1b60645f453c432cafc9898940d95eee,

title = "Magnetic Schr{\"o}dinger operators on periodic discrete graphs",

abstract = "We consider magnetic Schr{\"o}dinger 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 Schr{\"o}dinger 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 Schr{\"o}dinger operators constructed in the paper.",

keywords = "Discrete magnetic Schr{\"o}dinger operator, Flat bands, Periodic graph, Spectral bands",

author = "Evgeny Korotyaev and Наталья Сабурова",

year = "2017",

month = feb,

day = "15",

doi = "10.1016/j.jfa.2016.12.015",

language = "English",

volume = "272",

pages = "1625--1660",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "4",

}

RIS

TY - JOUR

T1 - Magnetic Schrödinger operators on periodic discrete graphs

AU - Korotyaev, Evgeny

AU - Сабурова, Наталья

PY - 2017/2/15

Y1 - 2017/2/15

N2 - 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.

AB - 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.

KW - Discrete magnetic Schrödinger operator

KW - Flat bands

KW - Periodic graph

KW - Spectral bands

UR - http://www.scopus.com/inward/record.url?scp=85007524152&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2016.12.015

DO - 10.1016/j.jfa.2016.12.015

M3 - Article

AN - SCOPUS:85007524152

VL - 272

SP - 1625

EP - 1660

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 4

ER -

ID: 35631742