Transport theory of coupled quantum dots based on the auxiliary-operator method

We formulate the theory of electron transport through coupled quantum dots by extending the auxiliary-operator representation. By using the generating functional technique, we derive the exact expressions for currents, dot-occupation numbers, and spin correlations, and examine them based on the nonequilibrium Green's function method under the noncrossing approximation (NCA). Our formulation generalizes the previous NCA approaches by allowing full occupation numbers with a finite Coulomb repulsion.