  The nonequilibrium Dyson (or Kadanoff-Baym) equation, which is an equation of
motion with long-range memory kernel for real-time Green functions, underlies
many numerical approaches based on the Keldysh formalism. In this paper we map
the problem of solving the Dyson equation in real-time onto a noninteracting
auxiliary Hamiltonian with additional bath degrees of freedom. The solution of
the auxiliary model does not require the evaluation of a memory kernel and can
thus be implemented in a very memory efficient way. The mapping is derived for
a self-energy which is local in space and is thus directly applicable within
nonequilibrium dynamical mean-field theory (DMFT). We apply the method to study
the interaction quench in the Hubbard model for an optical lattice with a
narrow confinement, using inhomogeneous DMFT in combination with second-order
weak-coupling perturbation theory. We find that, although the quench excites
pronounced density oscillations, signatures of the two-stage relaxation similar
to the homogeneous system can be observed by looking at the time-dependent
occupations of natural orbitals.
