Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers
Exner, Pavel ; Vugalter, Simeon
arXiv, 9709003 / Harvested from arXiv
Text on arXiv
We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary. If the windows are small enough, there is just one isolated eigenvalue. We find upper and lower asymptotic bounds on the gap between the eigenvalue and the essential spectrum in the planar case, as well as for N=1 in three dimensions. Based on these results, we formulate a conjecture on the weak-coupling asymptotic behaviour of such bound states.
Publié le : 1997-09-25
Classification:  Mathematics - Functional Analysis,  Mathematical Physics 
@article{9709003,
     author = {Exner, Pavel and Vugalter, Simeon},
     title = {Bound-state asymptotic estimates for window-coupled Dirichlet strips and
  layers},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9709003}
}

Exner, Pavel; Vugalter, Simeon. Bound-state asymptotic estimates for window-coupled Dirichlet strips and
  layers. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9709003/