Curvature-induced bound states for a $\delta$ interaction supported by a   curve in $\mathbb{R}^3$
  We study the Laplacian in $L^2(\mathbb{R}^3)$ perturbed on an infinite curve $\Gamma$ by a $\delta$ interaction defined through boundary conditions which relate the corresponding generalized boundary values. We show that if $\Gamma$ is smooth and not a straight line but it is asymptotically straight in a suitable sense, and if the interaction does not vary along the curve, the perturbed operator has at least one isolated eigenvalue below the threshold of the essential spectrum. 
Pavel Exner and Sylwia Kondej