The spectral shift function for planar obstacle scattering at low energy

Details The spectral shift function for planar obstacle scattering at low energy The spectral shift function for planar obstacle scattering at low energy

2011-11-18

arxiv.org/abs/1111.4377v1

Mathematics

Spectral Theory

Scientific paper

Let $H$ signify the free non-negative Laplacian on $\mathbb{R}^2$ and $H_Y$ the non-negative Dirichlet Laplacian on the complement $Y$ of a nonpolar compact subset $K$ in the plane. We derive the low-energy expansion for the Krein spectral shift function (scattering phase) for the obstacle scattering system $\{\,H_Y,\,H\,\}$ including detailed expressions for the first three coefficients. We use this to investigate the large time behaviour of the expected volume of the pinned Wiener sausage associated to $K$.

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