Francois Bentosela, Pierre Duclos, and Pavel Exner
Absolute continuity in periodic thin tubes and
strongly coupled leaky wires
(27K, LaTeX)
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 $\mathbb{R}^d,\: d=2,3$.