Pavel Exner and Milos Tater
Spectra of soft ring graphs
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ABSTRACT. We discuss of a ring-shaped soft quantum wire
modeled by $\delta$ interaction supported by the ring of a
generally nonconstant coupling strength. We derive condition which
determines the discrete spectrum of such systems, and analyze the
dependence of 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 investigated also 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