On the spectrum of curved quantum waveguides
Krejcirik, David ; Kriz, Jan
arXiv, 0306008 / Harvested from arXiv
Text on arXiv
The spectrum of the Laplace operator in a curved strip of constant width built along an infinite plane curve, subject to three different types of boundary conditions (Dirichlet, Neumann and a combination of these ones, respectively), is investigated. We prove that the essential spectrum as a set is stable under any curvature of the reference curve which vanishes at infinity and find various sufficient conditions which guarantee the existence of geometrically induced discrete spectrum. Furthermore, we derive a lower bound on the distance between the essential spectrum and the spectral threshold for locally curved strips. The paper is also intended as an overview of some new and old results on spectral properties of curved quantum waveguides.
Publié le : 2003-06-03
Classification:  Mathematical Physics,  Condensed Matter - Mesoscale and Nanoscale Physics,  Mathematics - Spectral Theory,  58J50, 35P15, 35Q40, 47A75, 49R50, 81Q10 
@article{0306008,
     author = {Krejcirik, David and Kriz, Jan},
     title = {On the spectrum of curved quantum waveguides},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306008}
}

Krejcirik, David; Kriz, Jan. On the spectrum of curved quantum waveguides. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306008/