  We study the non-equilibrium dynamics of a spinful single-orbital quantum dot
with an incorporated quantum mechanical spin-1/2 magnetic impurity. Due to the
spin degeneracy, double occupancy is allowed, and Coulomb interaction together
with the exchange coupling of the magnetic impurity influence the dynamics. By
extending the iterative summation of real-time path integrals (ISPI) to this
coupled system, we monitor the time-dependent non-equilibrium current and the
impurity spin polarization to determine features of the time-dependent
non-equilibrium dynamics. We particulary focus on the deep quantum regime,
where all time and energy scales are of the same order of magnitude and no
small parameter is available. We observe a significant influence of the
non-equilibrium decay of the impurity spin polarization both in the presence
and in the absence of Coulomb interaction. The exponential relaxation is faster
for larger bias voltages, electron-impurity interactions and temperatures. We
show that the exact relaxation rate deviates from the corresponding
perturbative result. In addition, we study in detail the impurity's back action
on the charge current and find a reduction of the stationary current for
increasing coupling to the impurity. Moreover, our approach allows us to
systematically distinguish mean-field Coulomb and impurity effects from the
influence of quantum fluctuations and flip-flop scattering, respectively. In
fact, we find a local maximum of the current for a finite Coulomb interaction
due to the presence of the impurity.
