  The Fermi liquid paradigm for metals has contributed enormously to our
understanding of condensed matter systems. However a growing number of quantum
critical systems have been shown to exhibit non Fermi liquid behavior. A full
understanding of such systems is still lacking and in particular analytical
results away from equilibrium are rare. In this work, we provide a distinct
example of such kind in a two channel Kondo Luttinger model where a Kondo
impurity couples to two voltage biased interacting electron leads,
experimentally realizable in a dissipative quantum dot. An exotic quantum phase
transition has been known to exist for two decades from the one channel to two
channel Kondo ground states by enhancing electron interactions in the leads,
but a controlled theoretical approach to this quantum critical point has not
yet been established. We present a controlled method to this problem and obtain
an analytical form for the universal nonequilibrium differential conductance
near the transition. The relevance of our results for recent experiments is
discussed.
