  We study the real-time dynamics of the Kondo effect after a quantum quench in
which a magnetic impurity is coupled to two metallic Hubbard chains. Using an
effective field theory approach, we find that for noninteracting electrons the
charge current across the impurity is given by a scaling function that involves
the Kondo time. In the interacting case, we show that the Kondo time decreases
with the strength of the repulsive interaction and the time dependence of the
current reveals signatures of the Kondo effect in a Luttinger liquid. In
addition, we verify that the relaxation of the impurity magnetization does not
exhibit universal scaling behavior in the perturbative regime below the Kondo
time. Our results highlight the role of nonequilibrium dynamics as a valuable
tool in the study of quantum impurities in interacting systems.
