Universality of the Kondo effect in a quantum dot out of equilibrium

We study the Kondo effect in a quantum dot subject to an external ac field. The Kondo effect can be probed by measuring the dc current induced by an auxiliary dc bias Vdc applied across the dot. In the absence of ac perturbation, the corresponding differential conductance G(Vdc) is known to exhibit a sharp peak at Vdc50, which is the manifestation of the Kondo effect. There exists only one energy scale, the Kondo temperature TK , which controls all the low-energy physics of the system; G is some universal function of eVdc /TK . We demonstrate that the dot driven out of equilibrium by an ac field is also characterized by a universal behavior: the conductance G depends on the ac field only through two dimensionless parameters, which are the frequency v and the amplitude of the ac perturbation, both divided by TK . We analytically find the largeand smallfrequency asymptotes of the universal dependence of G on these parameters. The obtained results allow us to predict the behavior of the conductance in the crossover regime \v;TK .