The Gross-Pitaevskii equation, a nonlinear Schr¨oedinger equation with non-zero boundary conditions, models superfluids and Bose-Einstein condensates. Recent mathematical work has focused on the finite-time dynamics of vortex solutions, and existence of vortex-pair traveling waves. However, little seems to be known about the long-time behaviour (eg. scattering theory, and the asymptotic stability of vortices). We address the simplest such problem – scattering around the vacuum state – which is already tricky due to the nonself-adjointness of the linearized operator, and ”long-range” nonlinearity. In particular, our present methods are limited to higher dimensions.