Scattering by local deformations of a straight leaky wire

Details Scattering by local deformations of a straight leaky wire Scattering by local deformations of a straight leaky wire

2004-10-03

arxiv.org/abs/math-ph/0410007v1

J. Phys. A38 (2005), 4865-4874

Physics

Mathematical Physics

Latex2e, 15 pages

Scientific paper

10.1088/0305-4470/38/22/011

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 $\alpha \to\infty$.

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