Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Bentosela, Francois; Duclos, Pierre; Exner, Pavel

Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Authors

Bentosela, Francois

Duclos, Pierre

Exner, Pavel

Description

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 Schrödinger operators with a sufficiently strongly attractive $δ$ interaction supported by a periodic curve in $\mathbb{R}^d, d=2,3$.
LaTeX 2e, 10 pages