Scattering problem for local perturbations of the free quantum gas

Scattering theory for perturbations of the intrinsic Dirichlet (Laplace-Bel trami) operator H-0 = - div(Gamma) del(Gamma) on L-2(Gamma, pi(z)) i. e. th e space of pi(z)-square integrable functions on the configuration space Gam ma over R-d, is studied. Here pi(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 Dir ichlet operators of perturbed Poisson measures instead of potential perturb ations 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 prove d.