  We study the time evolution of a half-filled Hubbard layer coupled to a
magnon bath after a quench of the Hubbard interaction. Qualitatively different
regimes, regarding the asymptotic long-time dynamics, are identified and
characterized within the mean-field approximation. In the absence of the bath,
the dynamics of the closed system is similar to that of a quenched BCS
condensate. Though the presence of the bath introduces an additional relaxation
mechanism, our numerical results and analytical arguments show that
equilibration with the bath is not necessarily attained within the
approximations used. Instead, nonequilibrium states, similar to the ones
observed in the closed system, can emerge at long times as a consequence of the
competition between the intrinsic relaxation mechanism (Landau damping, for
example), and the bath-induced dissipation.
