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In this report, we describe a recent development in a Fermi liquid theory forthe Kondo effect in quantum dots under a finite bias voltage $V$. Applying themicroscopic theory of Yamada and Yosida to a nonequilibrium steady state, wederive the Ward identities for the Keldysh Green's function, and determine thelow-energy behavior of the differential conductance $dI/dV$ exactly up to termsof order $(eV)^2$ for the symmetric Anderson model. These results are deducedfrom the fact that the Green's function at the impurity site is a functional ofa nonequilibrium distribution $f_{\text{eff}}(\omega)$, which at $eV=0$coincides with the Fermi function. Furthermore, we provide an alternativedescription of the low-energy properties using a renormalized perturbationtheory (RPT). In the nonequilibrium state the unperturbed part of the RPT isdetermined by the renormalized free quasiparticles, the distribution functionof which is given by $f_{\text{eff}}(\omega)$. The residual interaction betweenthe quasiparticles $\widetilde{U}$, which is defined by the full vertex part atzero frequencies, is taken into account by an expansion in the power series of$\widetilde{U}$. We also discuss the application of the RPT to a high-biasregion beyond the Fermi-liquid regime.Comment: 8 pages, to appear in a special edition of JPSJ "Kondo Effect -- 40  Years after the Discovery", typos are correcte

Fermi Liquid Theory for the Nonequilibrium Kondo Effect at Low Bias Voltages