  We consider the nonlinear Hartree equation for an interacting gas containing
infinitely many particles and we investigate the large-time stability of the
stationary states of the form $f(-\Delta)$, describing an homogeneous Fermi
gas. Under suitable assumptions on the interaction potential and on the
momentum distribution $f$, we prove that the stationary state is asymptotically
stable in dimension 2. More precisely, for any initial datum which is a small
perturbation of $f(-\Delta)$ in a Schatten space, the system weakly converges
to the stationary state for large times.
