The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces

0454087 - ÚJF 2016 RIV US eng J - Článek v odborném periodiku
Krejčiřík, David - Raymond, N. - Tušek, M.
The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces.
Journal of Geometric Analysis. Roč. 25, č. 4 (2015), s. 2546-2564. ISSN 1050-6926. E-ISSN 1559-002X
Grant CEP: GA ČR GAP203/11/0701
Grant ostatní: GA ČR(CZ) GA13-11058S
Institucionální podpora: RVO:61389005
Klíčová slova: curvature of hypersurfaces * effective potential * Eigenvalue asymptotics
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.109, rok: 2015

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.
Trvalý link: http://hdl.handle.net/11104/0254778