# Asymptotics of the Resonant Tunneling of High-Energy Electrons in Two-Dimensional Quantum Waveguides of Variable Cross-Section

Результат исследований: Научные публикации в периодических изданияхстатья

### Выдержка

A waveguide occupies a strip in ℝ 2 having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.

Язык оригинала английский 736-749 14 Journal of Mathematical Sciences (United States) 238 5 https://doi.org/10.1007/s10958-019-04271-4 Опубликовано - 7 мая 2019

### Отпечаток

Resonant tunneling
Waveguide
High Energy
Waveguides
Cross section
Electron
Resonator
Strip
Electrons
Resonators
Vertical angle
Helmholtz equation
Transmission Coefficient
Helmholtz Equation
Wave functions
Wave Function
Dirichlet Boundary Conditions
Boundary conditions
Transform
Eigenvalue

### Предметные области Scopus

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

### Цитировать

title = "Asymptotics of the Resonant Tunneling of High-Energy Electrons in Two-Dimensional Quantum Waveguides of Variable Cross-Section",
abstract = "A waveguide occupies a strip in ℝ 2 having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.",
author = "Sarafanov, {O. V.}",
year = "2019",
month = "5",
day = "7",
doi = "10.1007/s10958-019-04271-4",
language = "English",
volume = "238",
pages = "736--749",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer",
number = "5",

}

В: Journal of Mathematical Sciences (United States), Том 238, № 5, 07.05.2019, стр. 736-749.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Asymptotics of the Resonant Tunneling of High-Energy Electrons in Two-Dimensional Quantum Waveguides of Variable Cross-Section

AU - Sarafanov, O. V.

PY - 2019/5/7

Y1 - 2019/5/7

N2 - A waveguide occupies a strip in ℝ 2 having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.

AB - A waveguide occupies a strip in ℝ 2 having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.

UR - http://www.scopus.com/inward/record.url?scp=85064901371&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04271-4

DO - 10.1007/s10958-019-04271-4

M3 - Article

AN - SCOPUS:85064901371

VL - 238

SP - 736

EP - 749

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -