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Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections. / Kabardov, M. M.; Plamenevskii, B. A.; Sarafanov, O. V.; Sharkova, N. M.

In: Journal of Mathematical Sciences (United States), Vol. 238, No. 5, 07.05.2019, p. 641-651.

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

Harvard

Kabardov, MM, Plamenevskii, BA, Sarafanov, OV & Sharkova, NM 2019, 'Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections', Journal of Mathematical Sciences (United States), vol. 238, no. 5, pp. 641-651. https://doi.org/10.1007/s10958-019-04263-4

APA

Kabardov, M. M., Plamenevskii, B. A., Sarafanov, O. V., & Sharkova, N. M. (2019). Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections. Journal of Mathematical Sciences (United States), 238(5), 641-651. https://doi.org/10.1007/s10958-019-04263-4

Vancouver

Kabardov MM, Plamenevskii BA, Sarafanov OV, Sharkova NM. Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections. Journal of Mathematical Sciences (United States). 2019 May 7;238(5):641-651. https://doi.org/10.1007/s10958-019-04263-4

Author

Kabardov, M. M. ; Plamenevskii, B. A. ; Sarafanov, O. V. ; Sharkova, N. M. / Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections. In: Journal of Mathematical Sciences (United States). 2019 ; Vol. 238, No. 5. pp. 641-651.

BibTeX

@article{f119549c7f1548ba8e66402d8a17f307,
title = "Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections",
abstract = "The waveguide considered coincides with a strip having two narrows of width ε. An electron wave function satisfies the Dirichlet boundary value problem for the Helmholtz equation. The part of the waveguide between the narrows serves as a resonator, and conditions for the electron resonant tunneling may occur. In the paper, asymptotic formulas as ε → 0 for characteristics of the resonant tunneling are used. The asymptotic results are compared with the numerical ones obtained by approximate calculation of the scattering matrix for energies in the interval between the second and third thresholds. The comparison allows us to state an interval of ε, where the asymptotic and numerical approaches agree. The suggested methods can be applied to more complicated models than that considered in the paper. In particular, the same approach can be used for asymptotic and numerical analysis of the tunneling in three-dimensional quantum waveguides of variable cross-sections. Bibliography: 3 titles.",
author = "Kabardov, {M. M.} and Plamenevskii, {B. A.} and Sarafanov, {O. V.} and Sharkova, {N. M.}",
year = "2019",
month = may,
day = "7",
doi = "10.1007/s10958-019-04263-4",
language = "English",
volume = "238",
pages = "641--651",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "5",

}

RIS

TY - JOUR

T1 - Comparison of Asymptotic and Numerical Approaches to the Study of the Resonant Tunneling in Two-Dimensional Symmetric Quantum Waveguides of Variable Cross-Sections

AU - Kabardov, M. M.

AU - Plamenevskii, B. A.

AU - Sarafanov, O. V.

AU - Sharkova, N. M.

PY - 2019/5/7

Y1 - 2019/5/7

N2 - The waveguide considered coincides with a strip having two narrows of width ε. An electron wave function satisfies the Dirichlet boundary value problem for the Helmholtz equation. The part of the waveguide between the narrows serves as a resonator, and conditions for the electron resonant tunneling may occur. In the paper, asymptotic formulas as ε → 0 for characteristics of the resonant tunneling are used. The asymptotic results are compared with the numerical ones obtained by approximate calculation of the scattering matrix for energies in the interval between the second and third thresholds. The comparison allows us to state an interval of ε, where the asymptotic and numerical approaches agree. The suggested methods can be applied to more complicated models than that considered in the paper. In particular, the same approach can be used for asymptotic and numerical analysis of the tunneling in three-dimensional quantum waveguides of variable cross-sections. Bibliography: 3 titles.

AB - The waveguide considered coincides with a strip having two narrows of width ε. An electron wave function satisfies the Dirichlet boundary value problem for the Helmholtz equation. The part of the waveguide between the narrows serves as a resonator, and conditions for the electron resonant tunneling may occur. In the paper, asymptotic formulas as ε → 0 for characteristics of the resonant tunneling are used. The asymptotic results are compared with the numerical ones obtained by approximate calculation of the scattering matrix for energies in the interval between the second and third thresholds. The comparison allows us to state an interval of ε, where the asymptotic and numerical approaches agree. The suggested methods can be applied to more complicated models than that considered in the paper. In particular, the same approach can be used for asymptotic and numerical analysis of the tunneling in three-dimensional quantum waveguides of variable cross-sections. Bibliography: 3 titles.

UR - http://www.scopus.com/inward/record.url?scp=85064928050&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04263-4

DO - 10.1007/s10958-019-04263-4

M3 - Article

AN - SCOPUS:85064928050

VL - 238

SP - 641

EP - 651

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 41874280