  A combined nonequilibrium Green functions-Ehrenfest dynamics approach is
developed that allows for a time-dependent study of the energy loss of a
charged particle penetrating a strongly correlated system at zero and finite
temperature. Numerical results are presented for finite inhomogeneous
two-dimensional Fermi-Hubbard models, where the many-electron dynamics in the
target are treated fully quantum mechanically and the motion of the projectile
is treated classically. The simulations are based on the solution of the
two-time Dyson (Keldysh-Kadanoff-Baym) equations using the second-order Born,
third-order and T-matrix approximations of the self-energy. As application, we
consider protons and helium nuclei with a kinetic energy between 1 and 500
keV/u passing through planar fragments of the two-dimensional honeycomb lattice
and, in particular, examine the influence of electron-electron correlations on
the energy exchange between projectile and electron system. We investigate the
time dependence of the projectile's kinetic energy (stopping power), the
electron density, the double occupancy and the photoemission spectrum. Finally,
we show that, for a suitable choice of the Hubbard model parameters, the
results for the stopping power are in fair agreement with ab-initio simulations
for particle irradiation of single-layer graphene.
