The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides

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The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides. / Nazarov, S. A.

в: Sbornik Mathematics, Том 212, № 7, 9426, 07.2021, стр. 965-1000.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{2b9bd334d07441e29b4f8b2957e74187,

title = "The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides",

abstract = "Threshold resonance arises on the lower bound of the continuous spectrum of a quantum waveguide (the Dirichlet problem for the Laplace operator), provided that for this value of the spectral parameter a nontrivial bounded solution exists which is either a trapped wave decaying at infinity or an almost standing wave stabilizing at infinity. In many problems in asymptotic analysis, it is important to be able to distinguish which of the waves initiates the threshold resonance; in this work we discuss several ways to clarify its properties. In addition, we demonstrate how the threshold resonance can be preserved by fine tuning the profile of the waveguide wall, and we obtain asymptotic expressions for the near-threshold eigenvalues appearing in the discrete or continuous spectrum when the threshold resonance is destroyed.",

keywords = "Almost standing wave, Asymptotics, Boundary perturbation, Eigenvalue, Quantum waveguide, Threshold resonance, Trapped wave, trapped wave, threshold resonance, almost standing wave, boundary perturbation, quantum waveguide, TRANSMISSION, MODES, BOUND-STATES, asymptotics, eigenvalue",

author = "Nazarov, {S. A.}",

note = "Publisher Copyright: {\textcopyright} 2021 Russian Academy of Sciences (DoM) and London Mathematical Society",

year = "2021",

month = jul,

doi = "10.1070/sm9426",

language = "English",

volume = "212",

pages = "965--1000",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "7",

}

RIS

TY - JOUR

T1 - The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides

AU - Nazarov, S. A.

PY - 2021/7

Y1 - 2021/7

N2 - Threshold resonance arises on the lower bound of the continuous spectrum of a quantum waveguide (the Dirichlet problem for the Laplace operator), provided that for this value of the spectral parameter a nontrivial bounded solution exists which is either a trapped wave decaying at infinity or an almost standing wave stabilizing at infinity. In many problems in asymptotic analysis, it is important to be able to distinguish which of the waves initiates the threshold resonance; in this work we discuss several ways to clarify its properties. In addition, we demonstrate how the threshold resonance can be preserved by fine tuning the profile of the waveguide wall, and we obtain asymptotic expressions for the near-threshold eigenvalues appearing in the discrete or continuous spectrum when the threshold resonance is destroyed.

AB - Threshold resonance arises on the lower bound of the continuous spectrum of a quantum waveguide (the Dirichlet problem for the Laplace operator), provided that for this value of the spectral parameter a nontrivial bounded solution exists which is either a trapped wave decaying at infinity or an almost standing wave stabilizing at infinity. In many problems in asymptotic analysis, it is important to be able to distinguish which of the waves initiates the threshold resonance; in this work we discuss several ways to clarify its properties. In addition, we demonstrate how the threshold resonance can be preserved by fine tuning the profile of the waveguide wall, and we obtain asymptotic expressions for the near-threshold eigenvalues appearing in the discrete or continuous spectrum when the threshold resonance is destroyed.

KW - Almost standing wave

KW - Asymptotics

KW - Boundary perturbation

KW - Eigenvalue

KW - Quantum waveguide

KW - Threshold resonance

KW - Trapped wave

KW - trapped wave

KW - threshold resonance

KW - almost standing wave

KW - boundary perturbation

KW - quantum waveguide

KW - TRANSMISSION

KW - MODES

KW - BOUND-STATES

KW - asymptotics

KW - eigenvalue

UR - http://www.scopus.com/inward/record.url?scp=85116929397&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2711daa0-9722-38d7-b2b4-2323bc30bb89/

U2 - 10.1070/sm9426

DO - 10.1070/sm9426

M3 - Article

AN - SCOPUS:85116929397

VL - 212

SP - 965

EP - 1000

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 7

M1 - 9426

ER -

ID: 88365604