Geometrically induced spectrum in curved leaky wires

Details Geometrically induced spectrum in curved leaky wires Geometrically induced spectrum in curved leaky wires

2000-11-10

arxiv.org/abs/math-ph/0011015v1

J. Phys. A34 (2001), 1439-1450

Physics

Mathematical Physics

LaTeX2e, 16 pages

Scientific paper

10.1088/0305-4470/34/7/315

We study measure perturbations of the Laplacian in $L^2(\R^2)$ 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.

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