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Spectra of three-dimensional cruciform and lattice quantum waveguides. / Bakharev, F.L.; Matveenko, S.G.; Nazarov, S.A.

In: Doklady Mathematics, Vol. 92, No. 1, 2015, p. 514-518.

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

Harvard

Bakharev, FL, Matveenko, SG & Nazarov, SA 2015, 'Spectra of three-dimensional cruciform and lattice quantum waveguides', Doklady Mathematics, vol. 92, no. 1, pp. 514-518. https://doi.org/10.1134/S1064562415040274

APA

Bakharev, F. L., Matveenko, S. G., & Nazarov, S. A. (2015). Spectra of three-dimensional cruciform and lattice quantum waveguides. Doklady Mathematics, 92(1), 514-518. https://doi.org/10.1134/S1064562415040274

Vancouver

Bakharev FL, Matveenko SG, Nazarov SA. Spectra of three-dimensional cruciform and lattice quantum waveguides. Doklady Mathematics. 2015;92(1):514-518. https://doi.org/10.1134/S1064562415040274

Author

Bakharev, F.L. ; Matveenko, S.G. ; Nazarov, S.A. / Spectra of three-dimensional cruciform and lattice quantum waveguides. In: Doklady Mathematics. 2015 ; Vol. 92, No. 1. pp. 514-518.

BibTeX

@article{e3c7f3297bf346259ab97709180f81c4,
title = "Spectra of three-dimensional cruciform and lattice quantum waveguides",
abstract = "It is shown that the discrete spectrum of the Dirichlet problem for the Laplacian on the union of two mutually perpendicular circular cylinders consists of a single eigenvalue, while the homogeneous problem with a threshold value of the spectral parameter has no bounded solutions. As a consequence, an adequate one-dimensional model of a square lattice of thin quantum waveguides is presented and the asymptotic behavior of the spectral bands and lacunas (zones of wave transmission and deceleration) and the oscillatory processes they generate is described.",
author = "F.L. Bakharev and S.G. Matveenko and S.A. Nazarov",
year = "2015",
doi = "10.1134/S1064562415040274",
language = "English",
volume = "92",
pages = "514--518",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "1",

}

RIS

TY - JOUR

T1 - Spectra of three-dimensional cruciform and lattice quantum waveguides

AU - Bakharev, F.L.

AU - Matveenko, S.G.

AU - Nazarov, S.A.

PY - 2015

Y1 - 2015

N2 - It is shown that the discrete spectrum of the Dirichlet problem for the Laplacian on the union of two mutually perpendicular circular cylinders consists of a single eigenvalue, while the homogeneous problem with a threshold value of the spectral parameter has no bounded solutions. As a consequence, an adequate one-dimensional model of a square lattice of thin quantum waveguides is presented and the asymptotic behavior of the spectral bands and lacunas (zones of wave transmission and deceleration) and the oscillatory processes they generate is described.

AB - It is shown that the discrete spectrum of the Dirichlet problem for the Laplacian on the union of two mutually perpendicular circular cylinders consists of a single eigenvalue, while the homogeneous problem with a threshold value of the spectral parameter has no bounded solutions. As a consequence, an adequate one-dimensional model of a square lattice of thin quantum waveguides is presented and the asymptotic behavior of the spectral bands and lacunas (zones of wave transmission and deceleration) and the oscillatory processes they generate is described.

U2 - 10.1134/S1064562415040274

DO - 10.1134/S1064562415040274

M3 - Article

VL - 92

SP - 514

EP - 518

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 1

ER -

ID: 3944062