Nonequilibrium dynamical mean-field theory for bosonic lattice models

We develop the nonequilibrium extension of bosonic dynamical mean field theory (BDMFT) and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong coupling perturbative approaches, nonequilibrium BDMFT captures not only dynamical transitions, but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting both from the normal and Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in non-equilibrium "phase diagrams" which map out the different dynamical regimes.