 00473 D. Borisov, P. Exner, R. Gadylshin, D. Krejcirik
 Bound states in weakly deformed strips and layers
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Nov 30, 00

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Abstract. 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 threedimensional 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 weakcoupling
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 boundstate existence in the critical case when
the added volume is zero.
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