Curvature-induced bound states for a $\delta$ interaction supported by a curve in ${\mathbb{R}}^3$

Abstract

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.

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Cited by in corpus (17)

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