Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Details Absolute continuity in periodic thin tubes and strongly coupled leaky wires Absolute continuity in periodic thin tubes and strongly coupled leaky wires

2003-07-14

arxiv.org/abs/math/0307188v1

Lett. Math. Phys. 65 (2003), 75-82

Mathematics

Spectral Theory

LaTeX 2e, 10 pages

Scientific paper

10.1023/A:1027362115133

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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