Spectra of operator pencils with small PT-symmetric periodic perturbation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Spectra of operator pencils with small PT-symmetric periodic perturbation
Original language description
We study the spectrum of a quadratic operator pencil with a small P & xdcab;& x1d4af;& 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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
ISSN
1292-8119
e-ISSN
—
Volume of the periodical
26
Issue of the periodical within the volume
February
Country of publishing house
FR - FRANCE
Number of pages
32
Pages from-to
"Article Number: 21"
UT code for WoS article
000518022500002
EID of the result in the Scopus database
2-s2.0-85082082711