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- W2063332019 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 point-interaction 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." @default.
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- W2063332019 date "2003-09-23" @default.
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- W2063332019 title "Leaky quantum graphs: approximations by point-interaction Hamiltonians" @default.
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- W2063332019 doi "https://doi.org/10.1088/0305-4470/36/40/004" @default.
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