Scattering Problem for Local Perturbations\newline of the Free Quantum Gas
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Scattering theory for perturbations of the intrinsic Dirichlet (Laplace–Beltrami) operator H 0=−divΓ∇Γ on L 2(Γ,π z ), i. e. the space of π z -square integrable functions on the configuration space Γ over ℝ d , is studied. Here π z denotes Poisson measure with intensity z. We show that for an arbitrary regular non-zero potential V the standard wave operators W ±(H 0,H 0+V) do not exist, and propose to consider Dirichlet operators of perturbed Poisson measures instead of potential perturbations of the Hamiltonian H 0. As case studies, cylindric smooth densities and finite volume Gibbs perturbations of the Poisson measure are considered. In these cases the existence of the corresponding wave operators is proved.
KeywordsPotential Versus Integrable Function Finite Volume Configuration Space Wave Operator
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