Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window
Exner, P. ; Vugalter, S. A.
arXiv, 9602001 / Harvested from arXiv
Text on arXiv
Consider the Laplacian in a straight planar strip of width $\,d\,$, with the Neumann boundary condition at a segment of length $\,2a\,$ of one of the boundaries, and Dirichlet otherwise. For small enough $\,a\,$ this operator has a single eigenvalue $\,\epsilon(a)\,$; we show that there are positive $\,c_1,c_2\,$ such that $\,-c_1 a^4 \le \epsilon(a)- \left(\pi/ d\right)^2 \le -c_2 a^4\,$. An analogous conclusion holds for a pair of Dirichlet strips, of generally different widths, with a window of length $\,2a\,$ in the common boundary.
Publié le : 1996-02-02
Classification:  Mathematics - Functional Analysis,  Mathematical Physics 
@article{9602001,
     author = {Exner, P. and Vugalter, S. A.},
     title = {Asymptotic estimates for bound states in quantum waveguides coupled
  laterally through a narrow window},
     journal = {arXiv},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9602001}
}

Exner, P.; Vugalter, S. A. Asymptotic estimates for bound states in quantum waveguides coupled
  laterally through a narrow window. arXiv, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/9602001/