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

M. M. Kabardov, B. A. Plamenevskii, O. V. Sarafanov, N. M. Sharkova

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналаанглийский
Страницы (с-по)641-651
Число страниц11
ЖурналJournal of Mathematical Sciences (United States)
Том238
Номер выпуска5
DOI
СостояниеОпубликовано - 7 мая 2019

Отпечаток

Resonant tunneling
Waveguide
Waveguides
Cross section
Electron
Helmholtz equation
Dirichlet Boundary Value Problem
Interval
Asymptotic analysis
Electrons
Scattering Matrix
Bibliographies
Helmholtz Equation
Wave functions
Resonator
Asymptotic Formula
Asymptotic Analysis
Wave Function
Boundary value problems
Strip

Предметные области Scopus

  • Теория вероятности и статистика
  • Математика (все)
  • Прикладная математика

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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.",
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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.

В: Journal of Mathematical Sciences (United States), Том 238, № 5, 07.05.2019, стр. 641-651.

Результат исследований: Научные публикации в периодических изданияхстатья

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