Mathematics – Spectral Theory
Scientific paper
2005-08-26
Mathematics
Spectral Theory
AMSTeX, 22 pages
Scientific paper
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.
Exner Pavel
Frank Rupert L.
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