  We theoretically investigate the non-equilibrium quantum dynamical theory of
a quantum dot system coupled to fermionic reservoirs using the recently
developed stochastic fermionic quantum state diffusion (FQSD) equation. The
exact or approximate dynamical equations associated with the FQSD equation can
describe the non-equilibrium quantum transport processes beyond the long-time
limit leading to a steady state. We study in details the electron transport of
a quantum-dot system coupled to two fermionic environments with different
chemical potentials. We report the onset of Coulomb blockade in quantum dots in
two distinctive cases: one involving a spin degeneracy one-quantum dot model,
and the other a specific spin non-degeneracy two-quantum dot model. While the
spin degeneracy case shows that the current in the quantum dot may be blockaded
non-monotonically with respect to Coulomb energy, the non-degeneracy case
exhibits significant non-Markovian effects, and it enables us to study the
relations between initial conditions of the dots and the steady state currents.
