Geometrically induced spectrum in curved leaky wires

Abstract

We study measure perturbations of the Laplacian in $L^2({\mathbb{R}}^2)$ supported by an infinite curve $\Gamma$ in the plane which is asymptotically straight in a suitable sense. We show that if $\Gamma$ is not a straight line, such a ``leaky quantum wire'' has at least one bound state below the threshold of the essential spectrum.

LaTeX2e, 16 pages

Cited by in corpus (50)

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