 03275 Pavel Exner and Katerina Nemcova
 Title: Leaky quantum graphs: approximations
by point interaction Hamiltonians
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Jun 12, 03

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Abstract. We prove an approximation result showing how operators
of the type $\Delta \gamma \delta (x\Gamma)$ in
$L^2(\mathbb{R}^2)$, where $\Gamma$ is a graph, can be modeled in
the strong resolvent sense by pointinteraction Hamiltonians with
an appropriate arrangement of the $\delta$ potentials. The result
is illustrated on finding the spectral properties in cases when
$\Gamma$ is a ring or a star. Furthermore, we use this method to
indicate that scattering on an infinite curve $\Gamma$ which is
locally close to a loop shape or has multiple bends may exhibit
resonances due to quantum tunneling or repeated reflections.
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03275.tex