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.
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