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We theoretically investigate the non-equilibrium quantum dynamical theory ofa quantum dot system coupled to fermionic reservoirs using the recentlydeveloped stochastic fermionic quantum state diffusion (FQSD) equation. Theexact or approximate dynamical equations associated with the FQSD equation candescribe the non-equilibrium quantum transport processes beyond the long-timelimit leading to a steady state. We study in details the electron transport ofa quantum-dot system coupled to two fermionic environments with differentchemical potentials. We report the onset of Coulomb blockade in quantum dots intwo distinctive cases: one involving a spin degeneracy one-quantum dot model,and the other a specific spin non-degeneracy two-quantum dot model. While thespin degeneracy case shows that the current in the quantum dot may be blockadednon-monotonically with respect to Coulomb energy, the non-degeneracy caseexhibits significant non-Markovian effects, and it enables us to study therelations between initial conditions of the dots and the steady state currents.

Open system approach to non-equilibrium dynamical theory of quantum dot systems