On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021134" target="_blank" >RIV/62690094:18470/23:50021134 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1134/S0012266123020118" target="_blank" >https://link.springer.com/article/10.1134/S0012266123020118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1134/S0012266123020118" target="_blank" >10.1134/S0012266123020118</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity

Popis výsledku v původním jazyce

We consider the Schrodinger operator on the plane with bounded potential V-1(x) + V-2(y) + epsilon W(x, y), where V-1 is a real potential, V-2 and W are compactly supported complex potentials, and epsilon is a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrodinger operator H-1 = -d(2)/ dx(2) + V-1(x) consists of a pair of isolated eigenvalues and the essential spectrum of the operator H-2 = -d(2)/ dy(2)+V-2(y) has a virtual level at its lower edge and a spectral singularity inside. Additionally, we assume that there is a certain superposition of eigenvalues of the operator H-1 with the virtual level and spectral singularity of the operator H-2; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.

Název v anglickém jazyce

On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity

Popis výsledku anglicky

We consider the Schrodinger operator on the plane with bounded potential V-1(x) + V-2(y) + epsilon W(x, y), where V-1 is a real potential, V-2 and W are compactly supported complex potentials, and epsilon is a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrodinger operator H-1 = -d(2)/ dx(2) + V-1(x) consists of a pair of isolated eigenvalues and the essential spectrum of the operator H-2 = -d(2)/ dy(2)+V-2(y) has a virtual level at its lower edge and a spectral singularity inside. Additionally, we assume that there is a certain superposition of eigenvalues of the operator H-1 with the virtual level and spectral singularity of the operator H-2; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

DIFFERENTIAL EQUATIONS

ISSN

0012-2661

e-ISSN

1608-3083

Svazek periodika

59

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

5

Strana od-do

278-282

Kód UT WoS článku

000988284500011

EID výsledku v databázi Scopus

2-s2.0-85160648982