Absolute continuity in periodic thin tubes and strongly coupled leaky wires
نویسندگان
چکیده
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 Rd, d = 2, 3.
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