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Absolute continuity of the spectrum for periodically modulated leaky wires in R-3
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2007 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 8, no 2, 241-263 p.Article in journal (Refereed) Published
Abstract [en]

We consider a model of leaky quantum wires in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.

Place, publisher, year, edition, pages
2007. Vol. 8, no 2, 241-263 p.
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URN: urn:nbn:se:kth:diva-37009DOI: 10.1007/s00023-006-0307-3ISI: 000246110500002ScopusID: 2-s2.0-34247644889OAI: diva2:431816
Available from: 2011-07-26 Created: 2011-07-26 Last updated: 2011-07-26Bibliographically approved

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Frank, Rupert L.
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