Bound states in weakly deformed strips and layers
Borisov, D. ; Exner, P. ; Gadylshin, R. ; Krejcirik, D.
arXiv, 0011052 / Harvested from arXiv
Text on arXiv
We consider Dirichlet Laplacians on straight strips in R^2 or layers in R^3 with a weak local deformation. First we generalize a result of Bulla et al. to the three-dimensional situation showing that weakly coupled bound states exist if the volume change induced by the deformation is positive; we also derive the leading order of the weak-coupling asymptotics. With the knowledge of the eigenvalue analytic properties, we demonstrate then an alternative method which makes it possible to evaluate the next term in the asymptotic expansion for both the strips and layers. It gives, in particular, a criterion for the bound-state existence in the critical case when the added volume is zero.
Publié le : 2000-11-30
Classification:  Mathematical Physics 
@article{0011052,
     author = {Borisov, D. and Exner, P. and Gadylshin, R. and Krejcirik, D.},
     title = {Bound states in weakly deformed strips and layers},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0011052}
}

Borisov, D.; Exner, P.; Gadylshin, R.; Krejcirik, D. Bound states in weakly deformed strips and layers. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0011052/