Numerical Realization of Stochastic Dynamics of an Open Quantum-Dot System

 Master equation describes the time evolution of density matrix of a system. For a system of quantum dots, connected to two leads, working in many-body Fock space, we extend the Markovian, non-interacting, lowest order master equation to consider the effect of Coulomb interaction. However, the density matrix gives information about the expectation values and can not model the real stochastic process as measured in some experiments. By realizing our master equation with a stochastic piecewise deterministic process, we can simulate the real time evolution using random numbers. In order to further check the validity of our stochastic simulations, we compare the averaged results over time with the results obtained from stationary state density matrix and verify the consistency. Moreover, in a transport regime, using our numerical simulations we obtain the average flight time of electrons on QD and the the average time the QD remains empty and show that these times are inversely proportional to the tunneling rate between QD and leads.