  We prove a scattering result near certain steady states for a Hartree
equation for a random field. This equation describes the evolution of a system
of infinitely many particles. It is an analogous formulation of the usual
Hartree equation for density matrices. We treat dimensions 2 and 3, extending
our previous result. We reach a large class of interaction potentials, which
includes the nonlinear Schrodinger equation. This result has an incidence in
the density matrices framework. The proof relies on dispersive techniques used
for the study of scattering for the nonlinear Schrodinger equation, and on the
use of explicit low frequency cancellations as in the work of Lewin and Sabin.
To relate to density matrices, we use Strichartz estimates for orthonormal
systems from Frank and Sabin, and Leibniz rules for integral operators.
