| Abstract: | We discuss a ring-shaped soft quantum wire modelled by δ 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.
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