Approximations of quantum-graph vertex couplings by singularly scaled potentials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00208369" target="_blank" >RIV/68407700:21340/13:00208369 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/13:00395979
Result on the web
<a href="http://iopscience.iop.org/1751-8121/46/34/345202/pdf/1751-8121_46_34_345202.pdf" target="_blank" >http://iopscience.iop.org/1751-8121/46/34/345202/pdf/1751-8121_46_34_345202.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8113/46/34/345202" target="_blank" >10.1088/1751-8113/46/34/345202</a>

Result language
angličtina
Original language name
Approximations of quantum-graph vertex couplings by singularly scaled potentials
Original language description
We investigate the limit properties of a family of Schrodinger operators of the form H-epsilon = -d(2)/dx(2) + lambda(epsilon)/epsilon(2) Q(x/epsilon) acting on n-edge star graphs with the Kirchhoff interface conditions at the vertex. Here the real-valued potential Q has compact support and lambda(.) is analytic around epsilon = 0 with lambda(0) = 1. We show that if the operator has a zero-energy resonance of order m for epsilon = 1 and lambda(1) = 1, in the limit epsilon -> 0 one obtains the Laplacianwith a vertex coupling depending on 1 + 1/2m(2n - m + 1) parameters. We prove the norm-resolvent convergence as well as the convergence of the corresponding on-shell scattering matrices. The obtained vertex couplings are of scale-invariant type providedlambda' (0) = 0; otherwise the scattering matrix depends on energy and the scaled potential becomes asymptotically opaque in the low-energy limit.
Czech name
—
Czech description
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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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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