A Hardy inequality in twisted waveguides
2008 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 188, no 2, 245-264 p.Article in journal (Refereed) Published
We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.
Place, publisher, year, edition, pages
2008. Vol. 188, no 2, 245-264 p.
MAGNETIC SCHRÖDINGER OPERATOR, BOUND-STATES, SPECTRUM, EIGENVALUES, CURVATURE, TUBES
Other Physics Topics
IdentifiersURN: urn:nbn:se:kth:diva-6106DOI: 10.1007/s00205-007-0106-0ISI: 000254176700003OAI: oai:DiVA.org:kth-6106DiVA: diva2:10723
QC 20101007. Uppdaterad från accepted till published (20101007).2005-09-142005-09-142010-10-07Bibliographically approved