On absence of bound states for weakly attractive delta'-interactions supported on non-closed curves in R-2

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00458647" target="_blank" >RIV/61389005:_____/16:00458647 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/16:00304345
Result on the web
<a href="http://dx.doi.org/10.1063/1.4939749" target="_blank" >http://dx.doi.org/10.1063/1.4939749</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4939749" target="_blank" >10.1063/1.4939749</a>

Result language
angličtina
Original language name
On absence of bound states for weakly attractive delta'-interactions supported on non-closed curves in R-2
Original language description
Let Lambda subset of R-2 be a non-closed piecewise-C-1 curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let u(+/-)|(Lambda) is an element of L-2 (Lambda) be the traces of a function u in the Sobolev space H-1 (R-2 Lambda) onto two faces of.. We prove that for a wide class of shapes of Lambda the Schrodinger operator H-omega(Lambda) with delta'-interaction supported on. of strength omega is an element of L-infinity(Lambda;R) associated with the quadratic form H-1 (R-2 Lambda) q2 (sic) u bar right arrow integral(2)(R) vertical bar del u vertical bar(2) dx - integral(Lambda) omega vertical bar u(+)vertical bar(Lambda) - u(-)vertical bar Lambda vertical bar(2)ds has no negative spectrum provided that omega is pointwise majorized by a strictly positive function explicitly expressed in terms of Lambda. If, additionally, the domain R-2 Lambda is quasi-conical, we show that sigma(H-omega(Lambda)) = [0,+infinity). For a bounded curve. in our class and non-varying interaction strength omega is an element of R, we derive existence of a constant omega* > 0 such that sigma(H omega(Lambda)) = [0,+infinity) for all omega is an element of (-infinity,omega*]; informally speaking, bound states are absent in the weak coupling regime.
Czech name
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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
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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