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Nano device technology have been widely studied by many researchers. Quantum transport property is one of the fundamental problems because the systems of strongly correlated electrons and non equilibrium quantum statistical mechanics are achieved in nano devises. The d.c. current formulation is given as Landauer type formula using Keldysh green function [1]. This problem has been often investigated by Anderson model for the dilute impurity 3d transition metal in normal metal because conduction electrons flow though the small center region under the bias electrical potential. The difference of the two problems is the role of hybridization potential of the conduction electrons and the central region (impurity 3d atom), that is, the large hybridization is established when the central region is connected to the left or right electrode. On the other hand, for the impurity 3d atom and conduction electrons, the hybridization and Coulomb interaction are both essential to show the strong magnetization of impurity 3d atom. In the present study, we treat the d.c. current problem in Landauer type formula. Three parts are included in the model i.e. two electrodes and central small region where the hybridization potential Vp=L,R~k connects the conduction electron in each side (p =Left or Right). The switch of bias voltage is turned on and the hybridization is established. First, we calculate the d.c. current for non-interacting resonant level case which is simple model of a dot connected to the electrodes. Further, the interacting case is treated comparing to the non-interacting case by the perturbation theory about Coulomb interaction.

Calculation of d.c. Current in a Non-Interacting Resonant Level Model