We present a mode-coupling theory (MCT) for the high-density dynamics of two-dimensional spherical active Brownian particles (ABP). The theory is based on the integration-through-transients (ITT) formalism and hence provides a starting point for the calculation of non-equilibrium averages in active-Brownian particle systems. The ABP are characterized by a self-propulsion velocity v0, and by their translational and rotational diffusion coefficients, Dt and Dr. The theory treats both the translational and the orientational degrees of freedom of ABP explicitly. This allows to study the effect of self-propulsion of both weak and strong persistence of the swimming direction, also at high densities where the persistence length p = v0/Dr is large compared to the typical interaction length scale. While the low-density dynamics of ABP is characterized by a single Péclet number, Pe = v 2 0 /DrDt, close to the glass transition the dynamics is found to depend on Pe and p separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to sped up, while decreasing the persistence length slows down the relaxation. The theory predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, selfpropulsion velocity and rotational diffusivity. The active-MCT glass is a nonergodic state where correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.

The nonequilibrium time evolution of a quantum dot is studied by means of dynamic equations for timedependent Greens functions derived from a two-particle-irreducible (2PI) effective action for the Anderson impurity model. Coupling the dot between two leads at different voltages, the dynamics of the current through the dot is investigated. We show that the 2PI approach is capable to describe the dynamical build-up of the Kondo effect, which shows up as a sharp resonance in the spectral function, with a width exponentially suppressed in the electron self coupling on the dot. An external voltage applied to the dot is found to deteriorate the Kondo effect at the hybridization scale. The dynamic equations are evaluated within different nonperturbative resummation schemes, within the direct, particle-particle, and particle-hole channels, as well as their combination, and the results compared with that from other methods.