The low-energy properties of the Anderson impurity are studied under a finite bias voltage V using the perturbation theory in U of Yamada and Yosida in the nonequilibrium Keldysh diagrammatic formalism. The self-energy is calculated exactly up to terms of order ${\omega }^2,$ $T^2,$ and $V^2$ using Ward identities. The coefficients are defined with respect to the equilibrium ground state, and contain all contributions of the perturbation series in U. From these results, the nonlinear response of the current through the impurity has been deduced up to order $V^3.$

• Received 2 July 2001

DOI:https://doi.org/10.1103/PhysRevB.64.153305