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The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces
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SYSNO ASEP 0454087 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces Author(s) Krejčiřík, David (UJF-V) RID
Raymond, N. (FR)
Tušek, M. (CZ)Number of authors 3 Source Title Journal of Geometric Analysis. - : Springer - ISSN 1050-6926
Roč. 25, č. 4 (2015), s. 2546-2564Number of pages 19 s. Publication form Print - P Language eng - English Country US - United States Keywords curvature of hypersurfaces ; effective potential ; Eigenvalue asymptotics Subject RIV BE - Theoretical Physics R&D Projects GAP203/11/0701 GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000365472700020 EID SCOPUS 84948138228 DOI 10.1007/s12220-014-9525-y Annotation The Dirichlet Laplacian between two parallel hypersurfaces in Euclidean spaces of any dimension in the presence of a magnetic field is considered in the limit when the distance between the hypersurfaces tends to zero. We show that the Laplacian converges in a norm-resolvent sense to a Schrodinger operator on the limiting hypersurface whose electromagnetic potential is expressed in terms of principal curvatures and the projection of the ambient vector potential to the hypersurface. As an application, we obtain an effective approximation of bound-state energies and eigenfunctions in thin quantum layers. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2016
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