The spectral shift function for planar obstacle scattering at low energy

I E McGillivray

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arXiv · 1111.4377

The spectral shift function for planar obstacle scattering at low energy

I E McGillivray

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Abstract

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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BibTeX RIS

I E McGillivray. 2011-11-18. The spectral shift function for planar obstacle scattering at low energy. https://arxiv.org/abs/1111.4377

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