  We obtain and analyze the effect of electron-electron Coulomb interaction on
the time dependent current flowing through a mesoscopic system connected to
biased semi-infinite leads. We assume the contact is gradually switched on in
time and we calculate the time dependent reduced density operator of the sample
using the generalized master equation. The many-electron states (MES) of the
isolated sample are derived with the exact diagonalization method. The chemical
potentials of the two leads create a bias window which determines which MES are
relevant to the charging and discharging of the sample and to the currents,
during the transient or steady states. We discuss the contribution of the MES
with fixed number of electrons N and we find that in the transient regime there
are excited states more active than the ground state even for N=1. This is a
dynamical signature of the Coulomb blockade phenomenon. We discuss numerical
results for three sample models: short 1D chain, 2D lattice, and 2D parabolic
quantum wire.
