Motivated by recent experiments in ultracold atomic gases that explore the
nonequilibrium dynamics of interacting quantum many-body systems, we
investigate the nonequilibrium properties of a Fermi liquid. We apply an
interaction quench within the Fermi liquid phase of the Hubbard model by
switching on a weak interaction suddenly; then we follow the real-time dynamics
of the momentum distribution by a systematic expansion in the interaction
strength based on the flow equation method. In this paper we derive our main
results, namely the applicability of a quasiparticle description, the
observation of a new type of quasi-stationary nonequilibrium Fermi liquid like
state and a delayed thermalization of the momentum distribution. We explain the
physical origin of the delayed relaxation as a consequence of phase space
constraints in fermionic many-body systems. This brings about a close relation
to similar behavior of one-particle systems which we illustrate by a discussion
of the squeezed oscillator; we generalize to an extended class of systems with
discrete energy spectra and point out the generic character of the
nonequilibrium Fermi liquid results for weak interaction quenches. Both for
discrete and continuous systems we observe that particular nonequilibrium
expectation values are twice as large as their corresponding analogues in
equilibrium. For a Fermi liquid, this shows up as an increased
correlation-induced reduction of the quasiparticle residue in nonequilibrium.Comment: 54 page