  We consider the Hartree and Schr\"{o}dinger equations describing the time
evolution of wave functions of infinitely many interacting fermions in
three-dimensional space. These equations can be formulated using density
operators, and they have infinitely many stationary solutions. In this paper,
we prove the asymptotic stability of a wide class of stationary solutions. We
emphasize that our result includes Fermi gas at zero temperature. This is one
of the most important steady states from the physics point of view; however,
its asymptotic stability has been left open after Lewin and Sabin first
formulated this stability problem and gave significant results in their seminal
work [arXiv:1310.0604].
