Fermi liquid theory for the nonequilibrium Kondo effect at low bias voltages

In this paper, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage V. Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance dI/dV exactly up to terms of order (eV)(2) for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution f(eff)(omega), which at eV = 0 coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by f(eff)(omega). The residual interaction between the quasiparticles (U) over tilde, which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of (U) over tilde. We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.