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We consider the nonlinear Hartree equation for an interacting gas containinginfinitely many particles and we investigate the large-time stability of thestationary states of the form $f(-\Delta)$, describing an homogeneous Fermigas. Under suitable assumptions on the interaction potential and on themomentum distribution $f$, we prove that the stationary state is asymptoticallystable in dimension 2. More precisely, for any initial datum which is a smallperturbation of $f(-\Delta)$ in a Schatten space, the system weakly convergesto the stationary state for large times.

The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D