Absolute continuity of the spectrum for periodically modulated leaky wires in $\mathbb{R}^3$
Exner, Pavel ; Frank, Rupert L.
arXiv, 0508525 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-08-26
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  Mathematics - Analysis of PDEs,  Quantum Physics,  35P25, 81V99 
@article{0508525,
     author = {Exner, Pavel and Frank, Rupert L.},
     title = {Absolute continuity of the spectrum for periodically modulated leaky
  wires in $\mathbb{R}^3$},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508525}
}

Exner, Pavel; Frank, Rupert L. Absolute continuity of the spectrum for periodically modulated leaky
  wires in $\mathbb{R}^3$. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508525/