Asymptotics of resonant tunneling in a two-dimensional quantum waveguide with several equal resonators

Иван Анатольевич Гурьянов, Олег Васильевич Сарафанов

Research output

Abstract

The domain occupied by the waveguide is a strip with n+1 equal narrows of diameter ϵ. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation. Any part of the waveguide between two neighboring narrows plays the role of a resonator. Near a simple eigenvalue of the closed resonator, there are n resonant peaks of height close to 1. We let ϵ tend to 0 and obtain asymptotic formulas for the resonant values of the spectral parameter and for the widths of the resonant peaks at their half-height. The behavior of the transmission coefficient in a neighborhood of a resonance is described.
Original languageEnglish
Number of pages20
JournalApplicable Analysis
DOIs
Publication statusE-pub ahead of print - 8 Jun 2018

Fingerprint

Resonant tunneling
Resonator
Waveguide
Resonators
Waveguides
Helmholtz equation
Wave functions
Boundary value problems
Dirichlet Boundary Value Problem
Transmission Coefficient
Helmholtz Equation
Asymptotic Formula
Wave Function
Strip
Electrons
Tend
Electron
Eigenvalue
Closed

Scopus subject areas

  • Mathematics(all)

Cite this

@article{c5b837c44b454894aeaf4bc51b6b8f99,
title = "Asymptotics of resonant tunneling in a two-dimensional quantum waveguide with several equal resonators",
abstract = "The domain occupied by the waveguide is a strip with n+1 equal narrows of diameter ϵ. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation. Any part of the waveguide between two neighboring narrows plays the role of a resonator. Near a simple eigenvalue of the closed resonator, there are n resonant peaks of height close to 1. We let ϵ tend to 0 and obtain asymptotic formulas for the resonant values of the spectral parameter and for the widths of the resonant peaks at their half-height. The behavior of the transmission coefficient in a neighborhood of a resonance is described.",
keywords = "квантовый волновод, переменное сечение, уравнение Гельмгольца, резонансное туннелирование, асимптотическое описание, Quantum waveguide, variable cross-section, the Helmholtz equation, resonant tunneling, asymptotic description",
author = "Гурьянов, {Иван Анатольевич} and Сарафанов, {Олег Васильевич}",
year = "2018",
month = "6",
day = "8",
doi = "10.1080/00036811.2018.1478078",
language = "English",
journal = "Applicable Analysis",
issn = "0003-6811",
publisher = "Taylor & Francis",

}

TY - JOUR

T1 - Asymptotics of resonant tunneling in a two-dimensional quantum waveguide with several equal resonators

AU - Гурьянов, Иван Анатольевич

AU - Сарафанов, Олег Васильевич

PY - 2018/6/8

Y1 - 2018/6/8

N2 - The domain occupied by the waveguide is a strip with n+1 equal narrows of diameter ϵ. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation. Any part of the waveguide between two neighboring narrows plays the role of a resonator. Near a simple eigenvalue of the closed resonator, there are n resonant peaks of height close to 1. We let ϵ tend to 0 and obtain asymptotic formulas for the resonant values of the spectral parameter and for the widths of the resonant peaks at their half-height. The behavior of the transmission coefficient in a neighborhood of a resonance is described.

AB - The domain occupied by the waveguide is a strip with n+1 equal narrows of diameter ϵ. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation. Any part of the waveguide between two neighboring narrows plays the role of a resonator. Near a simple eigenvalue of the closed resonator, there are n resonant peaks of height close to 1. We let ϵ tend to 0 and obtain asymptotic formulas for the resonant values of the spectral parameter and for the widths of the resonant peaks at their half-height. The behavior of the transmission coefficient in a neighborhood of a resonance is described.

KW - квантовый волновод

KW - переменное сечение

KW - уравнение Гельмгольца

KW - резонансное туннелирование

KW - асимптотическое описание

KW - Quantum waveguide

KW - variable cross-section

KW - the Helmholtz equation

KW - resonant tunneling

KW - asymptotic description

U2 - 10.1080/00036811.2018.1478078

DO - 10.1080/00036811.2018.1478078

M3 - Article

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

ER -