### Abstract

Original language | English |
---|---|

Number of pages | 20 |

Journal | Applicable Analysis |

DOIs | |

Publication status | E-pub ahead of print - 8 Jun 2018 |

### Fingerprint

### Scopus subject areas

- Mathematics(all)

### Cite this

}

**Asymptotics of resonant tunneling in a two-dimensional quantum waveguide with several equal resonators.** / Гурьянов, Иван Анатольевич; Сарафанов, Олег Васильевич.

Research output

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 -