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ЖУРНАЛЫ // Наносистемы: физика, химия, математика // Архив

Наносистемы: физика, химия, математика, 2022, том 13, выпуск 2, страницы 156–163 (Mi nano1097)

Эта публикация цитируется в 1 статье

PHYSICS

On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field

A. S. Bagmutova, H. Najarb, I. F. Melikhova, I. Y. Popova

a ITMO University, St. Petersburg, 197101, Russia
b Département de Mathématiques, Faculté des Sciences de Moanstir. Avenue de l’environnement 5019 Monastir, Tunisie

Аннотация: The discrete spectrum of the Hamiltonian describing a quantum particle living in three dimensional straight layer of width $d$ in the presence of a constant electric field of strength $F$ is studied. The Neumann boundary conditions are imposed on a finite set of bounded domains (windows) posed at one of the boundary planes and the Dirichlet boundary conditions on the remaining part of the boundary (it is a reduced problem for two identical coupled layers with symmetric electric field). It is proved that such system has eigenvalues below the lower bound of the essential spectrum for any $F\ge0$. Then we closer examine a dependence of bound state energies on $F$ and window's parameters, using numerical methods.

Ключевые слова: quantum waveguide, Schrödinger operator, discrete spectrum.

Поступила в редакцию: 03.10.2021

Язык публикации: английский

DOI: 10.17586/2220-8054-2022-13-2-156-163



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