Spectral asymptotics of a strong delta ' interaction on a planar loop

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00209727" target="_blank" >RIV/68407700:21340/13:00209727 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/13:00395977
Result on the web
<a href="http://iopscience.iop.org/1751-8121/46/34/345201" target="_blank" >http://iopscience.iop.org/1751-8121/46/34/345201</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/46/34/345201" target="_blank" >10.1088/1751-8113/46/34/345201</a>

Result language
angličtina
Original language name
Spectral asymptotics of a strong delta ' interaction on a planar loop
Original language description
We consider a generalized Schrodinger operator in L-2(R-2) with an attractive strongly singular interaction of delta ' type characterized by the coupling parameter beta > 0 and supported by a C-4 smooth closed curve Gamma of length L without self-intersections. It is shown that in the strong-coupling limit, beta -> 0(+), the number of eigenvalues behaves as 2L/pi beta + O(vertical bar ln beta vertical bar), and furthermore, that the asymptotic behavior of the jth eigenvalue in the same limit is -4/beta(2) + mu(j) + O(beta vertical bar ln beta vertical bar), where mu(j) is the jth eigenvalue of the Schrodinger operator on L-2(0, L) with periodic boundary conditions and the potential -1/4 gamma(2), where gamma is the signed curvature of Gamma.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—

Project
<a href="/en/project/GAP203%2F11%2F0701" target="_blank" >GAP203/11/0701: Guided Quantum Dynamics</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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