Geometrically induced spectrum in curved leaky wires
  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. 
Pavel Exner and Takashi Ichinose