The spectral shift function for planar obstacle scattering at low energy

2011/11/18 by I. McGillivray, McGillivray, I E
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1111.4377

openalex publication_date 2011/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H signify the free non-negative Laplacian on ℝ² 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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