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The Magnetic Laplacian in Shrinking Tubular Neighborhoods of Hypersurfaces

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    0454087 - ÚJF 2016 RIV US eng J - Journal Article
    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
    R&D Projects: GA ČR GAP203/11/0701
    Grant - others:GA ČR(CZ) GA13-11058S
    Institutional support: RVO:61389005
    Keywords : curvature of hypersurfaces * effective potential * Eigenvalue asymptotics
    Subject RIV: BE - Theoretical Physics
    Impact factor: 1.109, year: 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.
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