Band gap of the Schrodinger operator with a strong delta-interaction on a periodic curve

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Band gap of the Schrodinger operator with a strong delta-interaction on a periodic curve
Original language description
In this paper we study the operator H-beta = -Delta - betadelta((.) - Gamma) in L-2(R-2), where Gamma is a smooth periodic curve in R-2. We obtain the asymptotic form of the band spectrum of H-beta as beta tends to infinity. Furthermore, we prove the existence of the band gap of sigma(H-beta) for sufficiently large beta >. 0. Finally, we also derive the spectral behaviour for beta - infinity in the case when Gamma is non-periodic and asymptotically straight.
Czech name
Lakuny Schrödingerova operátoru se silnou delta interakcí na periodické křivce
Czech description
V této práci studujeme operátor H.beta. = - .DELTA. - .beta. (. - .GAMMA.) v L2 (R2), kde .GAMMA. je hladká periodická křivka v R2. Získáme asymptotický tvar pásového spektra H.beta.

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)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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