On Occurrence of Resonances from Multiple Eigenvalues of the Schrödinger Operator in a Cylinder with Distant Perturbations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50018617" target="_blank" >RIV/62690094:18470/21:50018617 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10958-021-05532-x" target="_blank" >https://link.springer.com/article/10.1007/s10958-021-05532-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-021-05532-x" target="_blank" >10.1007/s10958-021-05532-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Occurrence of Resonances from Multiple Eigenvalues of the Schrödinger Operator in a Cylinder with Distant Perturbations

Popis výsledku v původním jazyce

In this paper, the Schrödinger operator with a localized potential in a multidimensional cylinder is considered. The boundary of the cylinder is split into three parts, two of which are “sleeves” going to infinity, and the third (central) part is located between them. On the sleeves and the central part, respectively, the Neumann and Dirichlet boundary conditions are posed. We examine the situation where the distance between the sleeves increases. We assume that the same Schrödinger operator in the same cylinder endowed with the Dirichlet condition on the whole boundary has an isolated double eigenvalue. We show that for a sufficiently large distance between the sleeves, this double eigenvalue splits into a pair of resonances of the original operator. For these resonances, we explicitly obtain the first terms of their asymptotic expansions and describe the behavior of the imaginary part of the resonances. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Název v anglickém jazyce

On Occurrence of Resonances from Multiple Eigenvalues of the Schrödinger Operator in a Cylinder with Distant Perturbations

Popis výsledku anglicky

In this paper, the Schrödinger operator with a localized potential in a multidimensional cylinder is considered. The boundary of the cylinder is split into three parts, two of which are “sleeves” going to infinity, and the third (central) part is located between them. On the sleeves and the central part, respectively, the Neumann and Dirichlet boundary conditions are posed. We examine the situation where the distance between the sleeves increases. We assume that the same Schrödinger operator in the same cylinder endowed with the Dirichlet condition on the whole boundary has an isolated double eigenvalue. We show that for a sufficiently large distance between the sleeves, this double eigenvalue splits into a pair of resonances of the original operator. For these resonances, we explicitly obtain the first terms of their asymptotic expansions and describe the behavior of the imaginary part of the resonances. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

—

Svazek periodika

258

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85115121070