  We study the dynamical behavior of doped electronic systems subject to a
global ramp of the repulsive Hubbard interaction. We start with formulating a
real-time generalization of the fluctuation-exchange approximation.
Implementing this numerically, we investigate the weak-coupling regime of the
Hubbard model both in the electron-doped and hole-doped regimes. The results
show that both local and nonlocal (momentum-dependent) observables evolve
toward a thermal state, although the temperature of the final state depends on
the ramp duration and the chemical doping. We further reveal a
momentum-dependent relaxation rate of the distribution function in doped
systems, and trace back its physical origin to the anisotropic self-energies in
the momentum space.
