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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 $K$.
Let $H_0 = -Delta + V_0(x)$ be a Schroedinger operator on $L_2(mathbb{R}^ u),$ $ u=1,2,$ or 3, where $V_0(x)$ is a bounded measurable real-valued function on $mathbb{R}^ u.$ Let $V$ be an operator of multiplication by a bounded integrable real-valued
This paper is a continuation of my previous work on absolutely continuous and singular spectral shift functions, where it was in particular proved that the singular part of the spectral shift function is an a.e. integer-valued function. It was also s
We consider the 3D Schrodinger operator $H_0$ with constant magnetic field $B$ of scalar intensity $b>0$, and its perturbations $H_+$ (resp., $H_-$) obtained by imposing Dirichlet (resp., Neumann) conditions on the boundary of the bounded domain $Ome
We consider the Schrodinger operator with constant magnetic field defined on the half-plane with a Dirichlet boundary condition, $H_0$, and a decaying electric perturbation $V$. We analyze the spectral density near the Landau levels, which are thresh
We consider the case of scattering of several obstacles in $mathbb{R}^d$ for $d geq 2$ for the Laplace operator $Delta$ with Dirichlet boundary conditions imposed on the obstacles. In the case of two obstacles, we have the Laplace operators $Delta_1$