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Spectra of soft ring graphs

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    0101841 - UJF-V 20043008 RIV GB eng J - Journal Article
    Exner, Pavel - Tater, Miloš
    Spectra of soft ring graphs.
    [Spektra měkkých prstencovýh grafů.]
    Waves in Random Media. Roč. 14, č. 1 (2004), S47-S60. ISSN 0959-7174
    R&D Projects: GA AV ČR IAA1048101
    Institutional research plan: CEZ:AV0Z1048901
    Keywords : strong delta-interaction * band-gap structure * schrodinger operator
    Subject RIV: BE - Theoretical Physics
    Impact factor: 1.558, year: 2004

    We discuss a ring-shaped soft quantum wire modelled by 6 interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.

    Byl studován měkký kvantový drát prstencovitého tvaru modelovaný 6ti interakcemi nesenými prstencem, obecně s nekonstantní vazbou. Byly diskutovány spektrální vlastnosti v závislosti na vazbách. Byl vyšetřován také systém vložený v homogenním magnetickém poli.
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