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

Asymptotic stability of a wide class of stationary solutions for the Hartree and Schr\"{o}dinger equations for infinitely many particles