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The time evolution of the out-of-equilibrium Mott insulator is investigatednumerically through calculations of space-time resolved density and entropyprofiles resulting from the release of a gas of ultracold fermionic atoms froman optical trap. For adiabatic, moderate and sudden switching-off of thetrapping potential, the out-of-equilibrium dynamics of the Mott insulator isfound to differ profoundly from that of the band insulator and the metallicphase, displaying a self-induced stability that is robust within a wide rangeof densities, system sizes and interaction strengths. The connection betweenthe entanglement entropy and changes of phase, known for equilibriumsituations, is found to extend to the out-of-equilibrium regime. Finally, therelation between the system's long time behavior and the thermalization limitis analyzed.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases