Bound states in weakly deformed strips and layers

Details Bound states in weakly deformed strips and layers Bound states in weakly deformed strips and layers

2000-11-30

arxiv.org/abs/math-ph/0011052v1

Ann. H. Poincare 2 (2001), 553-572

Physics

Mathematical Physics

LaTeX2e, 25 pages; to appear in Annales H. Poincare

Scientific paper

10.1007/PL00001045

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.

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