CURVATURE-INDUCED RESONANCES IN A 2-DIMENSIONAL DIRICHLET TUBE

Scattering problem is studied for the Dirichlet Laplacian in a curved planar strip which is assumed to fulfil some regularity and analyticit y requirements, with the curvature decaying as O (\s\(-1-epsilon)) for \s\ --> infinity. Asymptotic completeness of the wave operators is pr oven. If the strip width d is small enough we show that under the thre shold of the j-th transverse mode, j greater than or equal to 2, there is a finite number of resonances, with the poles approaching the real axis as d --> 0. A perturbative expansion for the pole positions is f ound and the Fermi-rule contribution to the resonance widths is shown to be exponentially small as d --> 0.