Dephasing and the steady state in quantum many-particle systems

We discuss relaxation in bosonic and fermionic many-particle systems. For integrable systems, the time evolution can cause a dephasing effect, leading for finite subsystems to certain steady states. We give an explicit derivation of those steady subsystem states and devise sufficient prerequisites for the dephasing to take place. We also find simple scenarios, in which dephasing is ineffective and discuss the dependence on dimensionality and criticality. It follows further that, after a quench of system parameters, bipartite entanglement entropy will become extensive. This provides a way of creating strong entanglement in a controlled fashion.