 04317 Pavel Exner and Sylwia Kondej
 Scattering by local deformations of a straight leaky wire
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Oct 3, 04

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Abstract. We consider a model of a leaky quantum wire with the
Hamiltonian $\Delta \alpha \delta(x\Gamma)$ in $L^2(\R^2)$,
where $\Gamma$ is a compact deformation of a straight line. The
existence of wave operators is proven and the Smatrix is found
for the negative part of the spectrum. Moreover, we conjecture
that the scattering at negative energies becomes asymptotically
purely onedimensional, being determined by the local geometry in
the leading order, if $\Gamma$ is a smooth curve and $\alpha
\to\infty$.
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