Schrödinger operators with singular interactions: a model of tunnelling resonances

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F04%3A00000757" target="_blank" >RIV/61389005:_____/04:00000757 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Schrödinger operators with singular interactions: a model of tunnelling resonances
Original language description
We discuss a generalized Schrodinger operator in L-2(R-d), d = 2, 3, with an attractive singular interaction supported by a (d - 1)-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky quantum wire and a family of quantum dots if d = 2, or surface waves in the presence of a finite number of impurities if d = 3. We analyse the discrete spectrum, and furthermore, we show that the resonance problem in this setting can be explicitly solved; by Birman-Schwinger method it is cast into a form similar to the Friedrichs model.
Czech name
Schrödingerovy operátory se singulárními interakcemi: model tunelové resonance
Czech description
Diskutujeme zobecněný Schrödingerův operátor v L2 (Rd), d=2,3, s přitažlivou singulární interakcí nesenou (d-1) rozměrnou nadrovinou a konečnou množinou bodů.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/IAA1048101" target="_blank" >IAA1048101: Quantum graphs and related systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2004
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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