03-325 Francois Bentosela, Pierre Duclos, and Pavel Exner

Absolute continuity in periodic thin tubes and strongly coupled leaky wires (27K, LaTeX) Jul 14, 03

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Abstract. Using 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 Schr\"odinger operators with a sufficiently strongly attractive $\delta$ interaction supported by a periodic curve in $\mathbb{R}^d,\: d=2,3$.

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