A REGULAR ANALOGUE OF THE SMILANSKY MODEL: SPECTRAL PROPERTIES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F17%3AA1801NVZ" target="_blank" >RIV/61988987:17310/17:A1801NVZ - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/17:00484251 RIV/68407700:21340/17:00319056
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A REGULAR ANALOGUE OF THE SMILANSKY MODEL: SPECTRAL PROPERTIES
Original language description
We analyze spectral properties of the operator $H=frac{partial^2}{partial x^2} -frac{partial^2}{partial y^2} +omega^2y^2-lambda y^2V(x y)$ in $L^2(mathbb{R}^2)$, where $omegane 0$ and $Vge 0$ is a compactly supported and sufficiently regular potential. It is known that the spectrum of $H$ depends on the one-dimensional Schr"odinger operator $L=-frac{mathrm{d}^2}{mathrm{d}x^2}+omega^2-lambdaV(x)$ and it changes substantially as $infsigma(L)$ switches sign. We prove that in the critical case, $infsigma(L)=0$, the spectrum of $H$ is purely essential and covers the interval $[0,infty)$. In the subcritical case, $infsigma(L)>0$, the essential spectrum starts from $omega$ and there is a non-void discrete spectrum in the interval $[0,omega)$. We also derive a bound on the corresponding eigenvalue moments.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
REP MATH PHYS
ISSN
0034-4877
e-ISSN
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Volume of the periodical
80
Issue of the periodical within the volume
2
Country of publishing house
PL - POLAND
Number of pages
16
Pages from-to
177-192
UT code for WoS article
000416194600004
EID of the result in the Scopus database
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