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We study thermalization in a one-dimensional quantum system consisting of anoninteracting fermionic chain with each site of the chain coupled to anadditional bath site. Using a density matrix renormalization group algorithm weinvestigate the time evolution of observables in the chain after a quantumquench. For low densities we show that the intermediate time dynamics can bequantitatively described by a system of coupled equations of motion. For higherdensities our numerical results show a prethermalization for local observablesat intermediate times and a full thermalization to the grand canonical ensembleat long times. For the case of a weak bath-chain coupling we find, inparticular, a Fermi momentum distribution in the chain in equilibrium in spiteof the seemingly oversimplified bath in our model.

Closed and Open System Dynamics in a Fermionic Chain with a Microscopically Specified Bath: Relaxation and Thermalization