  We study thermalization in a one-dimensional quantum system consisting of a
noninteracting fermionic chain with each site of the chain coupled to an
additional bath site. Using a density matrix renormalization group algorithm we
investigate the time evolution of observables in the chain after a quantum
quench. For low densities we show that the intermediate time dynamics can be
quantitatively described by a system of coupled equations of motion. For higher
densities our numerical results show a prethermalization for local observables
at intermediate times and a full thermalization to the grand canonical ensemble
at long times. For the case of a weak bath-chain coupling we find, in
particular, a Fermi momentum distribution in the chain in equilibrium in spite
of the seemingly oversimplified bath in our model.
