Quantum Joule expansions in one-dimensional lattices

We discuss the expansion dynamics of nonintegrable systems that contain bosons or fermions in one-dimensional lattices. The particles are initially confined in half of the system with a thermal state described by the canonical ensemble. At short times after we remove the barrier before the front hits the other boundary of the lattice, the radial velocity of the expansion is a constant. The center of mass is accelerated with a constant acceleration. At long times, local observables can be approximated by a thermal expectation of another canonical ensemble with an effective temperature. The weights for the diagonal ensemble and the canonical ensemble match well for high initial temperatures that correspond to negative effective final temperature after the expansion. The negative effective temperature for finite systems goes to positive inverse temperatures in the thermodynamic limit for bosons but is a true thermodynamic effect for fermions. We also compare the thermal entanglement entropy and density distribution in momentum space for the canonical ensemble, diagonal ensemble and instantaneous long-time states calculated by exact diagonalization.