 05290 Pavel Exner and Rupert L. Frank
 Absolute continuity of the spectrum for periodically modulated
leaky wires in R^3
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Aug 26, 05

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Abstract. We consider a model of leaky quantum wire in three dimensions. The
Hamiltonian is a singular perturbation of the Laplacian supported
by a line with the coupling which is bounded and periodically
modulated along the line. We demonstrate that such a system has a
purely absolutely continuous spectrum and its negative part has
band structure with an at most finite number of gaps. This result
is extended also to the situation when there is an infinite number
of the lines supporting the perturbations arranged periodically in
one direction.
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