Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F16%3AA1701IUR" target="_blank" >RIV/61988987:17310/16:A1701IUR - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/16:00458929 RIV/68407700:21340/16:00307467
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Spectral analysis of a class of Schrodinger operators exhibiting a parameter-dependent spectral transition
Original language description
We analyze two-dimensional Schrooedinger operators with the potential |xy|^p -lambda(x^2 +y^2)^{p/ (p+2)} where pge1 and lambdage0 which exhibit an abrupt change of spectral properties at a critical value of the coupling constant lambda. We show that in the supercritical case the spectrum covers the whole real axis. In contrast, for lambda below the critical value the spectrum is purely discrete and we establish a Lieb? Thirring-type bound on its moments. In the critical case where the essential spectrum covers the positive halfline while the negative spectrum can only be discrete, we demonstrate numerically the existence of a ground-state eigenvalue.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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