Strong Coupling Asymptotics for Schrödinger Operators with an Interaction Supported by an Open Arc in three Dimensions
Result description
We consider Schrodinger operators with a strongly attractive singular interaction supported by a finite curve Gamma of length L in R-3. We show that if Gamma is C-4-smooth and has regular endpoints, the j-th eigenvalue of such an operator has the asymptotic expansion lambda(j)(H-alpha,H-Gamma) = xi(alpha)+lambda(j)(S)+O(e(pi alpha)) as the coupling parameter alpha -> -infinity, where xi(alpha)= -4 e(2)(-2 pi alpha+psi(1)) and lambda(j)(S) is the j-th eigenvalue of the Schrodinger operator S = -d(2)/ds(2) - 1/4 gamma(2)(s) on L-2(0, L) with Dirichlet condition at the interval endpoints in which gamma is the curvature of Gamma.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/16:00307301
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Strong Coupling Asymptotics for Schrödinger Operators with an Interaction Supported by an Open Arc in three Dimensions
Original language description
We consider Schrodinger operators with a strongly attractive singular interaction supported by a finite curve Gamma of length L in R-3. We show that if Gamma is C-4-smooth and has regular endpoints, the j-th eigenvalue of such an operator has the asymptotic expansion lambda(j)(H-alpha,H-Gamma) = xi(alpha)+lambda(j)(S)+O(e(pi alpha)) as the coupling parameter alpha -> -infinity, where xi(alpha)= -4 e(2)(-2 pi alpha+psi(1)) and lambda(j)(S) is the j-th eigenvalue of the Schrodinger operator S = -d(2)/ds(2) - 1/4 gamma(2)(s) on L-2(0, L) with Dirichlet condition at the interval endpoints in which gamma is the curvature of Gamma.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reports on Mathematical Physics
ISSN
0034-4877
e-ISSN
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Volume of the periodical
77
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
1-17
UT code for WoS article
000371846500001
EID of the result in the Scopus database
2-s2.0-84959273825
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2016