Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires |
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| Authors: | Bentosela Francois Duclos Pierre Exner Pavel |
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| Institution: | (1) CNRS, Luminy Case 907, Centre de Physique Théorique, F-13288 Marseille Cedex 9, France;(2) Université de la Mediterranée (Aix–Marseille II), F-13288 Marseille, France;(3) PhyMat, Université de Toulon et du Var, BP 132, F-83957 La Garde Cedex, France;(4) Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences, CZ-25068 Rez near Prague, Czechia;(5) Doppler Institute, Czech Technical University, Brehová 7, CZ-11519 Prague, Czechia |
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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 Schrödinger operators with a sufficiently strongly attractive  interaction supported by a periodic curve in Rd = 2, 3. |
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| Keywords: | Schrö dinger operators singular interactions periodic systems absolute continuity |
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