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SchrÖdinger operators with guided potentials on periodic graphs. / Korotyaev, Evgeny; Сабурова, Наталья.

In: Proceedings of the American Mathematical Society, Vol. 145, No. 11, 01.01.2017, p. 4869-4883.

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

Harvard

Korotyaev, E & Сабурова, Н 2017, 'SchrÖdinger operators with guided potentials on periodic graphs', Proceedings of the American Mathematical Society, vol. 145, no. 11, pp. 4869-4883. https://doi.org/10.1090/proc/13733

APA

Korotyaev, E., & Сабурова, Н. (2017). SchrÖdinger operators with guided potentials on periodic graphs. Proceedings of the American Mathematical Society, 145(11), 4869-4883. https://doi.org/10.1090/proc/13733

Vancouver

Korotyaev E, Сабурова Н. SchrÖdinger operators with guided potentials on periodic graphs. Proceedings of the American Mathematical Society. 2017 Jan 1;145(11):4869-4883. https://doi.org/10.1090/proc/13733

Author

Korotyaev, Evgeny ; Сабурова, Наталья. / SchrÖdinger operators with guided potentials on periodic graphs. In: Proceedings of the American Mathematical Society. 2017 ; Vol. 145, No. 11. pp. 4869-4883.

BibTeX

@article{22ea3ce3b29940caaa89d43553a11da9,
title = "Schr{\"O}dinger operators with guided potentials on periodic graphs",
abstract = "We consider discrete Schr{\"o}dinger 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.",
keywords = "Discrete schr{\"o}dinger operator, Guided waves, Periodic graph",
author = "Evgeny Korotyaev and Наталья Сабурова",
year = "2017",
month = jan,
day = "1",
doi = "10.1090/proc/13733",
language = "English",
volume = "145",
pages = "4869--4883",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "11",

}

RIS

TY - JOUR

T1 - SchrÖdinger operators with guided potentials on periodic graphs

AU - Korotyaev, Evgeny

AU - Сабурова, Наталья

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Discrete schrödinger operator

KW - Guided waves

KW - Periodic graph

UR - http://www.scopus.com/inward/record.url?scp=85029582707&partnerID=8YFLogxK

U2 - 10.1090/proc/13733

DO - 10.1090/proc/13733

M3 - Article

AN - SCOPUS:85029582707

VL - 145

SP - 4869

EP - 4883

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -

ID: 35631589