Scattering problem for local perturbations of the free quantum gas (Q1302029)

Scattering theory was studied for different types of perturbations of the intrinsic Dirichlet operator \(H_0=-\text{div}^\Gamma\nabla^\Gamma\) on \(L_2(\Gamma,\pi_z)\), where \(\pi_z\) is the Poisson measure, \(\Gamma\) is the corresponding space, \(H_0\) the Hamiltonian of the corresponding system of the free Bose gas. For an arbitrary regular non-zero potential perturbation \(V\) the standard wave operators \(W^{\pm}(H_0,H_0+V)\) does not exist. A renormalization of the perturbed \(H_0+V\) can be given by the Dirichlet operator of the perturbed Poisson measure. Further, the local perturbation of the Poisson measure by a Gibbs factor describing locally perturbed Bose gas was considered.