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Asymptotic spectral analysis in colliding leaky quantum layers

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    0473567 - ÚJF 2018 RIV US eng J - Journal Article
    Kondej, S. - Krejčiřík, David
    Asymptotic spectral analysis in colliding leaky quantum layers.
    Journal of Mathematical Analysis and Applications. Roč. 446, č. 2 (2017), s. 1328-1355. ISSN 0022-247X. E-ISSN 1096-0813
    R&D Projects: GA ČR(CZ) GA14-06818S
    Institutional support: RVO:61389005
    Keywords : quantum layers * leaky graphs * Delta interaction supported on hypersurfaces * Norm-resolvent convergence * non-self-adjoint interaction
    Subject RIV: BE - Theoretical Physics
    OBOR OECD: Applied mathematics
    Impact factor: 1.138, year: 2017

    We consider the Schrodinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the hypersurfaces tends to zero. We establish the norm-resolvent convergence to a limiting operator and derive first-order corrections for the corresponding eigenvalues.
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