  We study non-equilibrium noise in Chiral Luttinger Liquids using the
Landauer-Buttiker Scattering approach, obtaining the current/voltage noise
spectrum for a four-terminal measurement scheme. Experimental consequences of
the tunneling of charges are present in the four-terminal measurement of both
the low-frequency shot noise ($\omega$ near 0), and the high-frequency
Josephson noise ($\omega$ near $\omega_J=e^*V/\hbar$). Within perturbation
theory, an algebraic singularity is present (to all orders) at the Josephson
frequency $\omega_J=e^*V/\hbar$, whose position depends on the charge $e^*$ of
the tunneling particles, either electrons or fractionally charged
quasiparticles. We show in a non-perturbative calculation for an exactly
solvable point that the singularity at the quasiparticle frequency exists only
in the limit of vanishing coupling, whereas the singularity at the electron
frequency is present for all coupling strengths. The vanishing coupling limit
corresponds to perfectly quantized Hall conductance in the case of
quasiparticle tunneling between edge states in the fractional quantum Hall
regime, and thus tunneling destroys the singularity at the quasiparticle
frequency concomitantly with the quantized current.
