  We calculate the finite-frequency current noise of a nonequilibrium
resonance-level quantum dot close to a dissipative quantum phase transition of
the Kosterlitz-Thouless (KT) type between a de-localized phase for weak
dissipation and a localized phase for strong dissipation. The resonance-level
is coupled to two spinless fermionic baths with a finite bias voltage and an
Ohmic boson bath representing the dissipative environment. The system is
equivalent to an effective anisotropic Kondo model out of equilibrium. To
compute the finite-frequency noise, we combine two recently developed
Functional Renormalization Group (FRG) approaches in Refs.[17,22] and in
Ref.[23]. The nonequilibrium current noise at zero-temperature and finite
frequencies shows a singular dip in the de-localized phase for the magnitude of
frequencies equal to the bias voltage; while the dip is smeared out as the
system moves to the localized phase. The corresponding peak-to-dip crossover is
found in the AC conductance for the magnitude of frequencies equal to the bias
voltage. The relevance and applications of our results for the experiments and
for tunnelings between Fractional Quantum Hall Edge (FQHE) states and chiral
Luttinger liquids are discussed.
