A magnetic version of the Smilansky-Solomyak model

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F17%3AA1801QYF" target="_blank" >RIV/61988987:17310/17:A1801QYF - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/17:00482519 RIV/68407700:21340/17:00319048
Result on the web
<a href="http://dx.doi.org/10.1088/1751-8121/aa9234" target="_blank" >http://dx.doi.org/10.1088/1751-8121/aa9234</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/aa9234" target="_blank" >10.1088/1751-8121/aa9234</a>

Result language
angličtina
Original language name
A magnetic version of the Smilansky-Solomyak model
Original language description
We analyze spectral properties of two mutually related families ofmagnetic Schr"{o}dinger operators, $H_{mathrm{Sm}}(A)=(i nabla+A)^2+omega^2 y^2+lambda y delta(x)$ and $H(A)=(i nabla+A)^2+omega^2 y^2+ lambda y^2 V(x y)$ in $L^2(R^2)$, with theparameters $omega>0$ and $lambda<0$, where $A$ is a vectorpotential corresponding to a homogeneous magnetic fieldperpendicular to the plane and $V$ is a regular nonnegative andcompactly supported potential. We show that the spectral propertiesof the operators depend crucially on the one-dimensionalSchr"{o}dinger operators $L= -frac{mathrm{d}^2}{mathrm{d}x^2}+omega^2 +lambda delta (x)$ and $L (V)= -frac{mathrm{d}^2}{mathrm{d}x^2} +omega^2 +lambda V(x)$,respectively. Depending on whether the operators $L$ and $L(V)$ arepositive or not, the spectrum of $H_{mathrm{Sm}}(A)$ and $H(V)$exhibits a sharp transition.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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