2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99377Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive $δ$ interaction supported by a periodic curve in $\mathbb{R}^d, d=2,3$.LaTeX 2e, 10 pagesSpectral TheoryMesoscale and Nanoscale PhysicsMathematical PhysicsQuantum Physics81V99text