A Born-Markov master equation approach to correlated quantum systems in non-equilibrium

The derivation of the Born-Markov master equation apt to describe open dissipative quantum systems in non-equilibrium is depicted and compared with the Lindblad formalism. Further it's extensions to quasi-degenerate states and it' evaluation in the system eigenbasis is given for the steady state in the wide band limit. In the second part the derivation of the self-consistent Born approach an improvement of the before discussed master equation is presented and explicit formulas for the calculation of the steady state and steady state current in a single quantum dot (Anderson Impurity) with spin dependent coupling is given. In the third part these two methods are numerically evaluated for the single quantum dot and the influence of temperature and coupling strength on the steady state and current characteristics is discussed. Further the quantum dot with spin-dependent coupling and a cyclic triple quantum dot are investigated to show current blocking effects and negative conductance due to Coulomb repulsion respectively quantum interference. The issue of quasi-degenerate states is discussed on the triple quantum dot by variation of gate voltages.