Pavel Exner and Sylwia Kondej
Scattering by local deformations of a straight leaky wire
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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 S-matrix is found
for the negative part of the spectrum. Moreover, we conjecture
that the scattering at negative energies becomes asymptotically
purely one-dimensional, being determined by the local geometry in
the leading order, if $\Gamma$ is a smooth curve and $\alpha
\to\infty$.