Approximation of quantum graph vertex couplings by scaled Schrodinger operators on thin branched manifolds
Result description
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann-type Laplacian on such manifolds is amended by suitable potentials, the resulting Schrodinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and make a conjecture that the same method can be applied to all couplings invariant with respect to the time reversal. We conclude with a result that certain vertex couplings cannot be approximated by a pure Laplacian.
Keywords
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/09:00159479
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Approximation of quantum graph vertex couplings by scaled Schrodinger operators on thin branched manifolds
Original language description
We discuss approximations of vertex couplings of quantum graphs using families of thin branched manifolds. We show that if a Neumann-type Laplacian on such manifolds is amended by suitable potentials, the resulting Schrodinger operators can approximate non-trivial vertex couplings. The latter include not only the delta-couplings but also those with wavefunctions discontinuous at the vertex. We work out the example of the symmetric delta'-couplings and make a conjecture that the same method can be applied to all couplings invariant with respect to the time reversal. We conclude with a result that certain vertex couplings cannot be approximated by a pure Laplacian.
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
LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A-Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
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Volume of the periodical
42
Issue of the periodical within the volume
41
Country of publishing house
GB - UNITED KINGDOM
Number of pages
22
Pages from-to
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UT code for WoS article
000270303300021
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2009