Spectra of operator pencils with small PT-symmetric periodic perturbation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017078" target="_blank" >RIV/62690094:18470/20:50017078 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.esaim-cocv.org/articles/cocv/pdf/2020/01/cocv190088.pdf" target="_blank" >https://www.esaim-cocv.org/articles/cocv/pdf/2020/01/cocv190088.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/cocv/2019070" target="_blank" >10.1051/cocv/2019070</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Spectra of operator pencils with small PT-symmetric periodic perturbation

Popis výsledku v původním jazyce

We study the spectrum of a quadratic operator pencil with a small P &amp; xdcab;&amp; x1d4af;&amp; xdcaf;-symmetric periodic potential and a fixed localized potential. We show that the continuous spectrum has a band structure with bands on the imaginary axis separated by usual gaps, while on the real axis, there are no gaps but at certain points, the bands bifurcate into small parabolas in the complex plane. We study the isolated eigenvalues converging to the continuous spectrum. We show that they can emerge only in the aforementioned gaps or in the vicinities of the small parabolas, at most two isolated eigenvalues in each case. We establish sufficient conditions for the existence and absence of such eigenvalues. In the case of the existence, we prove that these eigenvalues depend analytically on a small parameter and we find the leading terms of their Taylor expansions. It is shown that the mechanism of the eigenvalue emergence is different from that for small localized perturbations studied in many previous works.

Název v anglickém jazyce

Spectra of operator pencils with small PT-symmetric periodic perturbation

Popis výsledku anglicky

We study the spectrum of a quadratic operator pencil with a small P &amp; xdcab;&amp; x1d4af;&amp; xdcaf;-symmetric periodic potential and a fixed localized potential. We show that the continuous spectrum has a band structure with bands on the imaginary axis separated by usual gaps, while on the real axis, there are no gaps but at certain points, the bands bifurcate into small parabolas in the complex plane. We study the isolated eigenvalues converging to the continuous spectrum. We show that they can emerge only in the aforementioned gaps or in the vicinities of the small parabolas, at most two isolated eigenvalues in each case. We establish sufficient conditions for the existence and absence of such eigenvalues. In the case of the existence, we prove that these eigenvalues depend analytically on a small parameter and we find the leading terms of their Taylor expansions. It is shown that the mechanism of the eigenvalue emergence is different from that for small localized perturbations studied in many previous works.

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

2020

Kód důvěrnosti údajů

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

Název periodika

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS

ISSN

1292-8119

e-ISSN

—

Svazek periodika

26

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

32

Strana od-do

"Article Number: 21"

Kód UT WoS článku

000518022500002

EID výsledku v databázi Scopus

2-s2.0-85082082711