The spectrum of two quantum layers coupled by a window

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The spectrum of two quantum layers coupled by a window
Original language description
We consider the Dirichlet Laplacian in a domain formed by two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. Itis also shown that the eigenvalues emerge from the threshold of the essential spectrum as the window passes through certain critical shapes. We prove the necessary condition for the window to be of critical shape. Under an additional assumption we show that this condition is sufficient and obtain the asymptotic expansion for the emerging eigenvalue and for the associated eigenfunction.
Czech name
Spektrum dvou kvantových vrstev spojených oknem
Czech description
Studováno spektrum Dirichletova Laplacianu v oblasti tvořené dvěma trojrozměrnými paralelními vrstvami spojenými oknem. Ukázána existence vázaných stavů.

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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Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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